The Tottenham manager took umbrage with coverage of his team following Sunday's draw with Manchester United, but the West Ham boss feels he would have been better off staying mum.
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However, Allardyce feels that the former Porto coach should have shown more restraint and used the criticism in his favor.
"You can't do it," he told talkSPORT. "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 that he "admired" Villas-Boas's nerve but maintained that his response was ill-advised.
"However disappointed you may feel about what people say, in media terms, it's still much better keeping your powder dry," he said. "I admire him for having a go but I don't think it will do you any favors 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."