In a heated press conference that followed his side's 2-2 draw with Manchester United on Sunday, Villas-Boas hit out at what he perceived to be unfair coverage of Tottenham from certain sections of the media.
However, Allardyce feels the former Porto manager should have shown more restraint, and used the criticism in his favour.
Speaking to Talksport, Allardyce said: "You can't do it. You've got to take it on the chin.
"You have to use the criticism as a motivational drive to show these people that they are wrong.
"You, and your players, have got to do your talking on the field. I think he's just showed a little bit of immaturity.
"It can get under your skin, but you can't let that happen because you're not going to win."
Ahead of West Ham's encounter with Crystal Palace on Tuesday, Allardyce told reporters he "admired" Villas-Boas' nerve but maintained his response was ill-advised.
He added: "However disappointed you may feel about what people say in media terms, it's still much better keeping your powder dry.
"I admire him for having a go, but I don't think it will do you any favours in the end unfortunately.
"But I'd admire him for sticking up for himself and having a go for what he believes in. In all honesty, he's probably right."
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