Allardyce cupped his ear in disbelief at the end of Wednesday's 2-1 home win over Hull City as some fans voiced their disapproval over the manner of the result with boos.
West Ham were forced to hold on in the final stages against the 10 men of Hull, with the display drawing the ire of some of the Upton Park faithful, despite the fact the victory left them 11th in the Premier League and nine points clear of the relegation zone.
Allardyce insists he does not regret his gesture at the final whistle, and suggested fans should be more appreciative of his side's results.
"It's a small minority, but small minorities are good at voicing their opinion," he said on Saturday. "It's all borne out of frustration because they expected us to win more comfortably.
"Everybody in the cold light of day, when they calmed down, realised how important the win was, and everyone has to realise what we've done in the last eight games.
"We've taken 15 points in the last eight games - nearly two points per game - and that's about a top-six finish in the Premier League. At least a top-eight finish.
"So our form at the moment has never been as good, our results have never been as good at this stage of the season.
"We've beaten our points total in an eight-game spell. We've never done it before and we should all feel a little bit happier. I'm sure everyone who vented their frustration is happier we're nearer safety."
Allardyce went on to say the booing heard on Wednesday would not affect his relationship with the West Ham supporters.
"You have to accept your position is one where you'll be criticised and praised off and on," he said.
"You have to stay professional, keep your thick skin on and move on.
"It is very important to me to communicate with the fans and not hide what's going on behind the scenes.
"At the end of the day, we've had a difficult season. We plan to do better next season in the Premier League once we are safe."
