It is a different story if the circumstances allow prioritization, for example when your team leads by 10 points in the standings and can afford to give some of the best players a break, but they won't do this when it is still early in the season.
Even then, it's arguable whether resting some key players means they're not prioritizing the competition at all. You could argue that playing your best 11 for every game is detrimental to their stamina or something else.
That being said, I don't remember seeing any manager openly admits they don't give a damn about a competition. The closest I can think the claim that Ange told the board that Spurs should focus on winning the UEL last season because the EPL is a lost cause. I don't know if other managers have said the same thing for the UCL or not. If we're talking about a cup competition like the FA Cup, I guess there are some examples where you could argue the team doesn't take it seriously at all. CMIIW.