The Eagles’ 3-1 loss at Goodison Park on Saturday meant they are yet to pick the maximum points without the former Manchester United winger since September 2016.
But the manager insisted they lost the duel due to ‘defensive mistakes’ rather than the absence of Zaha who is sidelined with a knee injury he suffered last week against Newcastle United.
“We didn’t lose because we were lacking players because the XI was a good XI but we lost because we were punished for the defensive mistakes we made,” Allardyce said.
“It was not because we were totally outplayed and not because Zaha did not play.”
Goals from Gylfi Sigurdsson, Oumar Niasse and Tom Davies were enough to see the Everton defeat Crystal Palace who got a late consolatory effort via Luka Milivojevic’s penalty.
According to Hodgson, Zaha is going to be back in action sooner than expected after the Cote d’Ivoire international had been feared out of the season.