The Hammers boss acknowledged in his programme notes that this has been a "testing campaign", adding he can understand the supporters' frustration having failed to pick up a point in April.
That run saw the pressure mount on Allardyce, who was subjected to chants and banners during last weekend's defeat at West Brom.
Those same supporters, however, will have been in a better mood on Saturday as a Harry Kane own goal shortly after Younes Kaboul saw red and Stewart Downing's free-kick saw West Ham run out 2-0 victors against Spurs, their third success of the season over the north London club.
"One week you are not playing so well and people sound off their disapproval, which they are quite entitled to do, like I've always said that," Allardyce said.
"But they do get behind you when they've got something to get behind. They don't stop singing, the players enjoyed being here, they enjoyed playing on this stage today, which is what we want them to do.
"We don't want to be fearful when we go out and they really gave a wholehearted performance to lift everybody today on the last game of the season. We couldn't have asked for anything more than what we got today.
"I thought it would be wonderful if we could do the treble, particularly under the circumstances as we haven't won for four games. To do it for the third occasion in our last home game and do it with an excellent performance by all the players.
"I know they went down to 10 men, but to take full advantage of that as well was a fantastic day for us, a great performance to finish the season here and send the fans home happy.
"The fans were right behind the team from start to finish because they knew the team was playing well and deserved a victory in the end.
"But for Hugo Lloris, I think we would have had for more than 2-0. That is more than satisfying for us, though, against a team fighting to be in the Champions League, fighting to get in that area."