Allardyce delighted with West Ham showing
The hosts completed the league double over Spurs at Upton Park thanks to a Harry Kane own-goal and Stewart Downing's free kick.
Both goals came after Younes Kaboul was sent off for a foul on Downing, and Allardyce, whose side also beat Spurs in the League Cup, felt the period after his dismissal was "critical".
The victory secured West Ham's top-flight status and put a dent in Spurs European hopes, with Allardyce also suggesting that his side could have won by a greater margin.
"But for (Hugo) Lloris I think it would have been far more than 2-0, but that's more than satisfying for us against a team who are fighting to get into (Europe)," he said.
"To beat them here and do the double over them is a great, great thing for us.
"We got the sending off, deservedly so, because Stewart was going one-on-one with the goalkeeper.
"The good thing for us was taking advantage of that and getting that goal within two minutes and from there we really took the game to Tottenham.
"Scoring the goal before half-time was a critical time as well and we were even more relaxed and created even more chances in the second half but sadly we didn't convert any because of that goalkeeper.
"He must have pulled off at least fix or six top-class saves."