Of course it does. It effects the amount of time a manager has to prepare for the next game; the opposition has had at least 3-4 more days to review videos, coach the players, find weaknesses and so on.
When at Southampton Poch use to have a practise match Mid-week, to put into practise the tactics he had been teaching them through training. This is no longer possible due to Europa League, as he has to prepare a completely different group of players for a different game, before getting back on Friday-Sat and having 1 day to prepare the squad.
There's been several times this year when we've played 11 reserves in EL and looked shit on the Weekend. It's not down to tired players, it's down to lack of preparation and a fatigued coaching team.
So what is the excuse for how terribly we've played since we left Europa. I think your point would hold some water if the end of our season had been extremely positive, but we've looked worse since Fiorentina than we did in August and September.