I don't think it was Mourinho.I know that in England FA cup is the most valued cup by all the teams because they a couple of other cups going but not as famous as this one,this is the most important one,we saw that with lower league teams beating the hell out of Premier League sides and this says a lot about the importance of such cup.You may think that these Premier League sides underestimated the value of this cup but this is not the reality,the reality is that they were found unprepared during such matches and that is why it is better to bet both teams to score rather than money lines here,a lot of surprise results.
It was so important even in Asia that before satelite tv came with all the live shows, national TV and radio even broadcast FA Cup programmes including prematch discussions and it was a big thing that everyone would play to win.
It changed after Champions League qualification was more "valuable" than FA Cup (which doesn't qualify you).
Also lower side PL teams prefer to fight survival (and keep earning more money) than to win FA Cup.
I definitely think some teams no longer value this cup.