Liverpool manager Rafa Benitez claimed Bolton were a bunch of divers after Monday's 2-2 draw at The Reebok ended their 10-game winning run.
But Allardyce said: "We were a bunch of cast-offs and freebies up against a side put together for a lot of money who became European champions.
"We led them twice and in the end got a draw. This is what upsets bigger managers and bigger teams.
"They cannot cope with how well we do on such little resources.
"If they don't get a win it is an easy excuse for them to make about our supposed tactics."
Bolton have been roundly accused of being over-physical and a long-ball team - something Allardyce refutes.
He said: "We might not be able to compete with the likes of Liverpool when it comes to skill and money.
"But we are fit, tactically well organised and determined.
"So many other people go on about how we play and if enough people say it everyone will start believing it.
"To call us a long-ball team is totally unfair on me and the players we have here who can play different styles. We have some great footballers and great passers.
"But because we are Bolton, people cannot accept it when we equal Liverpool in a one-on-one match."