Despite all the recent negativity, Spurs head into this weekend's London derby sitting fourth in the table and five points adrift of leaders Manchester City.
The former England boss was correct in one sense, as his side were only undone by a couple of goals from the title-chasing Blues in the final 25 minutes at Stamford Bridge, a week after holding Arsenal to a 2-2 draw, but the Eagles have now ultimately taken just five points from their past 10 league matches.
That run of form is simply not good enough, leaving the South London outfit 14th in the table and just two points above the dropzone, and an EFL Cup exit at the hands of second-tier side Middlesbrough last Wednesday did not help matters.
Palace's biggest problem has been on home soil, where the surprise draw against in-form Arsenal saw them pick up only a second point of the season from a possible 15 - the worst-such return of any side in the top flight.
Five matches without a win at Selhurst Park is the Eagles' longest run at the start of a season since 1997-98, when going 15 games without picking up three points, and things do not get any easier this weekend with the visit of fourth-placed Tottenham.
Either side of the creditable draw with Arsenal, Palace have lost to Bournemouth, Wolverhampton Wanderers, Everton and Chelsea in the Premier League, as well as going down to Middlesbrough in the EFL Cup. From 14 games overall this season, meanwhile, they have won just four.
Hodgson knows that a lack of goals, and an over-reliance on star man Wilfried Zaha, has all too often cost his side this term, with a tally of eight eight goals scored - Zaha responsible for three of those - the fifth-worst record in the division.
With Tottenham and Manchester United up next for Palace, on top of meetings with Man City and Chelsea in December, Hodgson needs his side to turn their so-called promising displays into all three points if they are to avoid dropping below the dotted line.
Recent form in Premier League: DLLLDL
Recent form (all competitions): LLLDLL
Following on from bad results against PSV Eindhoven in the Champions League and Man City in the Premier League, Tottenham have got their campaign right back on track over the past week-and-a-half with three wins on the spin.
West Ham United were brushed aside in the last 16 of the EFL Cup and Wolves were just about held off in last week's top-flight clash, before earning a crucial 2-1 win at home to PSV on Tuesday to revive their European hopes.
Spurs still require a minor miracle of sorts if they are to make it through to the knockout stages of the Champions League, but Harry Kane's latest brace in midweek did at least end a poor run of form on the continent and sets Tottenham up nicely for games against Inter Milan and Barcelona.
All focus for now is on their domestic hopes, though, and Tottenham are still very much in the mix at the top end of the division, despite Mauricio Pochettino himself recently admitting that the mood has been as low as he can remember - at least before this recent upturn in fortunes.
The ongoing uncertainty over when exactly the Lilywhites will move into their new home, combined with a lack of ambition during the summer transfer window, means that Pochettino has been swimming against the tide pretty much from the opening day of the season.
Credit to the players, then, for winning eight of their first 11 matches, which leaves Spurs in a healthy position. Six of those victories have come away from Wembley, including in each of their last four, giving them the best away record of any side in the league.
In fact, Pochettino's men have won more away matches in 2018 than any other Premier League side, with their tally of 11 victories being bettered only once before in their history - coming in 1960 when winning 17 times on their travels.
Tottenham have also picked up victory in their last five London derbies, seeing off Fulham and West Ham so far this term for their best-such run since between October 1950 and August 1951, when winning eight on the bounce against fellow clubs from the capital.
If that was not reason enough to fancy Spurs this weekend, Pochettino has won eight Premier League matches against Palace - against no other side has he managed more, level with Swansea City.
Recent form in Premier League: WWWWLW
Recent form (all competitions): WDLWWW
Wanyama is in contention to return to the squad this weekend, but it may well be that Christian Eriksen is again used in a deeper midfield position alongside Harry Winks, who stood out in the PSV win.
One man who is certain of a starting spot is Kane, who has 24 goals in 37 London derbies in the Premier League - a ratio of 0.65 goals per game that only Arsenal legend Thierry Henry, with 43 in 59, can better.
Hodgson has no fresh injury concerns on the back of the loss at Stamford Bridge, though, and despite going down 3-1 the experienced manager may well go with the same XI that started that one.
Andros Townsend ended his long run without a league goal and Zaha again showed why Tottenham reportedly wanted to sign him in the summer, while at the other end of the field Wayne Hennessey continues to do enough to keep hold of the number-one shirt.
Crystal Palace possible starting lineup:
Hennessey; Wan-Bissaka, Tomkins, Sakho, Van Aanholt; McArthur, Kouyate, Milivojevic, Meyer; Zaha, Townsend
Tottenham Hotspur possible starting lineup:
Lloris; Trippier, Alderweireld, Sanchez, Davies; Winks, Eriksen; Lamela, Lucas, Son; Kane
Head To Head
Palace have lost their last six top-flight games against Tottenham, scoring just once across those matches.
Against only two Premier League sides have Spurs had a longer winning, winning seven in a row against Man City (between 2004 and 2007) and Swansea (between 2012 and 2015).
Twenty-five of the 26 goals scored in Prem games between Palace and Tottenham have arrived in the second half, with just one first-half goal in the last 14 encounters.
We say: Crystal Palace 0-2 Tottenham Hotspur
Tottenham will be desperate to keep their momentum going with a fourth win on the spin, as they are thrown right in at the deep end after the international break with games against Chelsea, Inter Milan and Arsenal in quick succession. Closing the gap on the top three will be the target for Pochettino, and everything points towards what should be another away victory on Saturday.