Bale made his comeback off the bench but missed a chance to kill the game as Spurs collapsed despite leading through Heung-min Son and a Harry Kane double.
Fabian Balbuena and an own goal from Davinson Sanchez got West Ham back in it late on before Lanzini struck a stunning stoppage-time equaliser.
Mourinho said: “I think you can imagine how frustrated I am. It was exactly when we were in control that we conceded the first and their belief went up.
"My guys were not strong enough to cope with it psychologically.
“The last few seconds we lost two points. This is a game that was in the pocket and we lost two points.
“It’s difficult to say complacency. To be critical at that level. A team that scores three goals like we did cannot lose like we did.
“They were lucky but maybe they deserved that luck. We were unlucky but maybe we deserved that.
"Harry Kane hit the post. Bale can score the fourth and kill it. Based on free-kicks and second balls, they found a style. We should be stronger.”
West Ham became the first team in Premier League history to avoid defeat in a game having trailed by three or more goals as late as the 81st minute.
Hammers boss David Moyes said: “I have just seen my celebration... a David Pleat moment came to mind. My players were all laughing at me!
“I know someone else who has run and slid down the touchline, so I wasn't going to copy that.”