Tottenham manager Andre Villas-Boas criticised the White Hart Lane fans last weekend for not being patient enough as his side tried to break down a Hull side with a massed defence looking to break on the counter.
But Allardyce, whose West Ham side were drawn against Spurs in the League Cup quarter-finals, said: "They (Tottenham) do the same when they play in Europe.
"Chelsea will go away and play the same way at Schalke and play on the break. Manchester United will go away and play the same way.
"They all know that they play that way themselves so they can't really criticise the team that comes to them and sits behind the ball because they do the same in the bigger games, especially in the Champions League.
"So when you hear a manager moaning about that, he should really watch what he is saying because when it comes around and he does it he wants to get some praise for what he does, particularly if he ends up with a result or winning.
"We all have to tactically set out how to nullify the opposition."
Allardyce faces an Aston Villa side on Saturday perfectly suited to a counter-attacking style and he is mindful of the fact that West Ham have lost three league matches so far this season at Upton Park.
Allardyce said: "We are one of those teams who are struggling with points on the board. All that matters at the end is winning matches. Last season at home was a fantastic ride for us. This season it has been bitterly disappointing.
"The players are bound to feel extra pressure and feel more anxious but they have to remind themselves of the good performances they've given and continue in that vein from a confidence point of view.
"We have been severely punished for not taking chances."
Matthew Taylor misses out after suffering a knock in the League Cup victory against Burnley while Mladen Petric is also out for a couple of weeks after aggravating an injury in an Under 21 run-out. Ricardo Vaz Te misses out, too, after dislocating a shoulder against Swansea on Sunday.
Allardyce, however, is confident his side - when the squad is fully-fit - will start to surge up the Premier League table and believes they have a good chance of beating Tottenham and going all the way in the League Cup.
"On the night you have to have your team spot on," Allardyce added. "You have to have your team get a bit of luck and you have to make sure you get through.
"Andre will have his problems because he is still playing Europa League football on top of Premier League football on top of Capital One Cup next round.
"There is no doubt we will make some changes in our team that we play against them and I'm sure that they will.
"They have obviously invested in a huge squad now, spending £100million. So I suppose the pressure is more on them than us because they are supposed to be able to cope with it more than we are."
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