In contrast to Lambert, Mourinho said the tournament has a "special feeling" to it and stated that winning the FA Cup at Wembley in 2007 was one of the highest points of his managerial career.
"The FA Cup has a special feeling, a special meaning," Mourinho said.
"I was lucky to win lots of trophies but to win the FA Cup at Wembley and feel what it means was one of my high moments in my career.
"I have a good feeling for the competition and the good things this country has in terms of football I think we have to keep them.
"I don't agree (with Lambert), but Paul has the right to express his opinion and he has a right to think differently than I think. And I have the right to think differently than he does.
"Especially for teams without European competition, where they play 38 matches during a (Premier League) season, and where FA Cup matches come not in midweek matches but one more weekend with football, I don't see a reason for the clubs for not trying to win matches."
Mourinho sees no reason why clubs not involved in European competition do not take the FA Cup seriously, unlike Lambert whose primary focus remains on the Premier League.
And speaking before Saturday's third-round game with Sheffield United, Lambert was asked whether the FA Cup was something Premier League clubs could do without.
"If they were being honest, they probably would do," Lambert said.
"If you can get through, then absolutely I want to get through, I don't want to not get through, but your main one is the league.
"It is realistic. That is the nature of it. If anyone says any differently, then I am not so sure they will be telling the truth because the Premier League is the most vital thing that anyone wants to get into and we are no different."