Mourinho has taken some flak this season for Manchester United’s defensive performances, especially after the 0-0 draw against Liverpool at Anfield.
Some fans have claimed the Portuguese is not playing the ‘Manchester United way’ of fast, attacking football.
But Allardyce says playing like that is harder than ever before because of the rise in transfer fees.
He believes United fans will not care about the style of football their side play if they go on to win major honours under Mourinho.
“He’s a very clever man,” Allardyce said of Mourinho on beIN Sports.
“His approach is that this is what he is and ‘this is what I do to win you trophies and this is how I win you trophies’.
“You know what he his before he arrives so if a club like Manchester United want trophies, he’s the best man to deliver those trophies.
“If you’re criticising the way you play, or the way he plays, then that’s the way he knows how to get the team and squad he has to win things.
“He’s proven that at Chelsea twice, (Inter) Milan, Real Madrid and I’m sure that eventually he’ll prove that to be at Manchester United.
“Manchester United fans when they win a trophy or win a league won’t be too worried about Jose Mourinho’s tactics, believe you me, even for a club with such a stellar history.”