Although Everton are 10th in the table, they sit just four points above Palace and seven clear of the relegation zone. The Norwegian forward Alexander Sorloth impressed both defensively and in attack, but was unable to register his name on the scoresheet.
Gylfi Sigurdsson, Oumar Niasse, and Tom Davies all found the net to secure a comfortable win despite Luka Milivojevic scoring a late penalty for the Eagles.
He said: "Surprised, very surprised".
"The good thing is we have two weeks before we play the next game, which will allow the players with injuries and fatigue to recover and get ready for Watford [on 24 February]".
Are Everton already eyeing up a replacement for Sam Allardyce?
"Only I would know that because it's my job to study the whole game".
"It's a blip that we have to get over quickly", he said.
Hodgson admitted that the goals his side conceded were a result of poor defending.
Indeed, the Everton boss instead sought to accentuate the positives of a second-half performance he believes saw his team outplay the Gunners. "While it's much more important you do it here in front of your home fans than away, even though we've got great away support, there's 30-odd thousand here so when you make them happy, that's what you're here for".
"To be honest we didn't lose today because we were lacking players, we lost because we were punished for the defensive mistakes that we made. There was a spirited recovery by the players that is forgotten about when you see 5-1 but we need to react properly". I would have thought Mangala will be the less serious of the two injuries.