Pickford failed to reach Bruno Fernandes' shot as United equalised following an early goal gifted to Everton by their keeper David De Gea.
Here, the PA news agency looks at the men putting pressure on Pickford – and, in one case, De Gea too – for a starting place.
Pope top of the stops
Keeping the opposition out remains the most important job for a goalkeeper and England boss Gareth Southgate will be keenly aware that Burnley's Nick Pope leads all Premier League goalkeepers with 11 clean sheets this season.
That is one more than Liverpool's Alisson Becker and two clear of the nearest English challengers, Dean Henderson and Ben Foster – indeed, in Europe's "big five" leagues, only Real Madrid's Thibaut Courtois (12) has more than Pope.
Henderson has excelled on loan at Sheffield United, suggesting he may have a long-term role to play for his parent club Manchester United, while former international Foster's form has been crucial to Watford's resurgence after a woeful start to the season.
Pickford ranks fourth among English keepers but only joint-11th in the Premier League with six clean sheets, with four apiece for outside-chance candidates Tom Heaton (Aston Villa), Alex McCarthy (Southampton) and Aaron Ramsdale (Bournemouth).
Ramsdale ranks third in the Premier League with 95 saves, behind Newcastle's runaway leader Martin Dubravka (112) and Arsenal's Bernd Leno (97), but Henderson comes out on top in terms of save percentage.
The 22-year-old has faced 86 shots on target this season and let in just 22 goals for a save percentage of 74.4 – bettered only by Alisson, Tottenham's Hugo Lloris and Crystal Palace pair Vicente Guaita and Wayne Hennessey, with the latter playing just twice.
Pope (86 of 124) and Ramsdale (95 of 137) have each saved almost 70 per cent, with Pickford's 63 per cent rate also ranking below Foster, Heaton and McCarthy and 24th out of 35 keepers in this season's top flight.
'Pick' that out
The official Premier League website marks Pickford as being responsible for three errors leading to opposing goals this season and though Everton have won one and drawn two of the games in question, concerns remain.
The 25-year-old flapped at a Newcastle corner under pressure from Florian Lejeune before the defender scored the first of his two stoppage-time goals in the Magpies' stunning comeback at Goodison Park in January.
Two games later he allowed Christian Benteke's shot underneath him at the near post – a mistake Pickford himself labelled "disgusting" – though Everton still went on to beat Crystal Palace 3-1.
He admitted he was out of position as Fernandes' goal made it three from Pickford errors in Everton's last five games, and both club and country must hope it is just a short-term dip.
Henderson coming for De Gea?
Earlier in the Everton-United game, the hosts took the lead when De Gea cleared the ball against onrushing striker Dominic Calvert-Lewin and saw it rebound straight into the net.
Like Pickford, De Gea was committing his third "error leading to a goal" in this season's premierleague.com statistics – most notably letting a shot from Watford's Ismaila Sarr squirt straight through his hands at the near post in December.
Henderson had his own horror moment against Liverpool in September, allowing Georginio Wijnaldum's winner through his arms and legs, but has responded well and recently told Sport24's Kelly and Wrighty Show that his "big dream" is to break into the United first team.
Leading De Gea in clean sheets, goals conceded and save percentage and with only that one costly error marked against his name, Henderson is building a strong case to achieve that aim.