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.
The bad results currently being faced cannot be separated from several problems currently being faced. They have difficulty getting good chemistry between players, player injuries also greatly influence Manchester United performance in the UCL and EPL. They have been eliminated from the UCL, now is the time for Ten Hag to make changes to improve MU performance to keep the team able to compete again in the top four.
Manchester United can perform even better if they find chemistry with each other, the players they currently have are very high quality. Ten Hag still has the opportunity to rebuild trust between his fellow players to get positive results.