Two goals in the space of six second-half minutes from Ricardo Vaz Te and Gary O'Neil saw off Posh as the Hammers closed in on second-placed Reading ahead of a mouth-watering Saturday meeting between the two teams.
But the win was marred by negative chants about Allardyce's perceived direct style of play which rung out from the visiting supporters.
The Hammers boss said: "The perception of some people is deluded as the facts about my teams clearly speak for themselves.
"It is a tag that has followed me around for a long time and one I'm never going to be able to shift. I can't do anything about that but I can win football matches.
"We have had to overcome home teams playing with a lot of energy in front of full houses throughout this season. We did it again here and once we got the goals, we out-passed and outplayed Peterborough.
"It was a good performance, although not as good as at Burnley on Saturday. We only drew that game though so everyone was miserable whereas they will be happy."
Posh boss Darren Ferguson said: "We paid the price for not scoring when we were having the better of the game. If George (Boyd) had taken that chance right on the stroke of half-time, I feel sure we would have gone on to win.
"We should have had a penalty just before that and I feel sure it would have been given had it happened in the other area, but the really disappointing thing was the way in which we reacted to going behind.
"Too many players went into their shells and you can't afford to do that against any team, let alone one aiming to return to the Premier League."