"You can't do it," Allardyce 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."
Villas-Boas's spat came after his side drew 2-2 with Manchester United.