Manchester United got a big shock in Champions League that can trigger a domino effect on their next performances. However it won't always happen and sometimes, a team in trouble can strongly bounce back but we won't know how Manchester United will perform in Premier League after disappointed in Champions League.
In general you are right that a team may make come back in local league after bad result in bigger league or vice versa but Manchester United seems to be a different case. They have not shown their best performance yet in both competitions. After they were eliminated from UCL, they have to face Liverpool in the next match. Unfortunately they have to play without their captain due to yellow card accumulation as well as some players who may not play due to injuries such as Luke Shaw and Maguire. Some other players may not be able to play as well such as Rashford and Martial unless these players can get quick recovery. It will be hard match for Man United to set the best possible lineups and strategy against Liverpool.
But it should be that with Man Utd ending in the UCL, this could make Ten Heg focus more on making the best strategy for Man Utd in the Premier League. Because now Man Utd only has to focus on the Premier League. And this I think is 1 positive thing. Although I'm still not sure whether Man Utd will improve or not. But if Man Utd still performs badly in the Premier League. So I think we have to really give up to see Man Utd rise this season. Unless there is a change of coach. The day after tomorrow Man Utd will face Liverpool. And maybe in this match Man Utd will really be in trouble. Because their current condition is not very hopeful. There are many factors that make Man Utd not be favourites. One of them is as you mentioned. Plus, Liverpool is the host for this match. So this will only encourage Liverpool to play more aggressively than usual.