Following the game, Allardyce was surprised of the reaction from the Goodison faithfuls.
"It's a blip that we have to get over quickly", he said.
The visitors had taken a first-half lead through a classy goal by Jose Izquierdo on 32 minutes, but Xherdan Shaqiri equalised for much-improved Stoke midway through the second half.
That form line is starting to really test the patience of the Eagles fans, and a lot of them have run out of it where the striker is concerned.
That was an titillating pre-amble to this occasion and until the second half, their spat was the most entertaining thing about this fixture.More news: Team USA Announces Its Flag Bearer: Luger Erin Hamlin
Allardyce confirmed the trip will be after Tuesday night's EitC event at St George's Hall, saying: "Normally we would go after the game but the Gala Dinner is so important to the club and Everton in the Community, they do a fantastic job".
Everton climbed to ninth and the only negative on an otherwise impressive afternoon was Luke Milivojevic's late consolation from the penalty spot.
Allardyce next faces his former club managed by another former England manager in Roy Hodgson and he believes the absence of forward Wilfried Zaha, ruled out for a month with a knee injury, could give Everton the edge.
Another game without a goal means that the 27-year-old has now scored just twice in 21 appearances in the Premier League for Palace this season.
"We need to avoid the threat of relegation and it needs to start with Crystal Palace", Allardyce said.
"I was a bit disappointed we didn't get the clean sheet but I thought we were defensively solid and we found a way to take our chances in the second half".