Allardyce was appointed as Everton manager in November after Ronald Koeman was sacked
The Toffees started reasonably well and had the ball in the Spurs net when Wayne Rooney diverted new signing Cenk Tosun’s header beyond Hugo Lloris, only for the goal to be ruled out for offside.
Moments later, they were behind when Son Heung-min tapped in Serge Aurier’s cross-cum-shot to give Mauricio Pochettino’s side the lead.
Just after the break, Harry Kane doubled Spurs’ lead but replays show that the striker was stood in an offside position.
The Toffees’ play seriously declined from that point and Kane made it 3-0 before Christian Eriksen completed the rout following a expert team goal by Spurs late on.
Defeat sees Everton without a win in their last six games in all competitions, having been unbeaten in Allardyce’s first six games in charge on the club.
And Allardyce, who spoke to talkSPORT’s Sam Matterface after the game, said he was “massively disappointed” with his side’s reaction to going 2-0 down early in the second half.
Allardyce said: “I can’t take any positives from the game and I’m shocked. I’m really shocked at what I’ve seen.
“I thought Tottenham’s second goal was offside but we can’t control that.
“But I’m massively upset and massively disappointed in the reaction to going 2-0 down. It’s a complete lack of discipline and a lack of fight to get back into the game. That was the biggest disappointment of all.
“You have to accept that responsibility and that criticism and I will accept it too for turning a team out that performed like that in the second-half.
“It’s very difficult for me to understand why because I haven’t seen any of that since I have been here and I’ll work hard to make sure that it doesn’t happen again.”