Villas-Boas responded angrily to the recent negative press he has received after Spurs drew 2-2 with Manchester United in Sunday's Barclays Premier League clash at White Hart Lane.
Allardyce believes the comments were ill-advised and urged the Spurs manager to keep his own counsel.
"You have to use the criticism as a motivational drive to show these people that they are wrong. You've got to take it on the chin," Allardyce told talkSPORT.
"You and your players have got to do your talking on the field. I think he's just shown 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."
Shortly after giving the radio interview, Allardyce took a more sympathetic approach towards Villas-Boas when speaking to the press ahead of Tuesday night's clash with Crystal Palace.
"I've haven't read about Andre Villas-Boas' comments, but I've obviously heard about them," Allardyce said.
"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."