Palace did restore just a little pride after the restart at the Emirates Stadium, however, scoring the only goal of the second half through a Luka Milivojevic strike to offer Hodgson some encouragement.
Speaking to the assembled press after the 4-1 loss, the 70-year-old said: "The game was over very early for us. Two-nil after seven or eight minutes at the Emirates against Arsenal is not a good position to be in.
"At half time I thought we were staring down the barrel of the gun. A team of Arsenal's quality, with the players they've got, four goals up can't possibly lose. It was just a question of 'how many do we want to score'?
"Had we not marshalled ourselves and shown the character the players showed in the second half, the desire and produced work-rate and energy they did in the second half it would have been an avalanche.
"We stopped them scoring more goals and reduced the deficit to minus three rather than minus seven or minus eight."
The defeat for Palace was just their second in 13 Premier League games, with both coming against Arsenal.