He was put on the sidelines by Fergie.
The same happened with Moyes.
The same was going to happen with LvG.
When 3 managers in succession all feel that a player is not good enough, we need to accep that he wasn't good enough.
No thanks, I don't need to accept anything. Fergie didn't really use him, even Moyes didn't have an in form Kagawa and LVG certainly didn't.
If a player hasn't played first team football with any consistency, confidence or support for a couple of years they aren't going to be at their best. Under Fergie he did get games but he didn't get long runs of games, rarely in his best position but also with a team playing ever worse. He wasn't remotely close to his best form by the time Moyes took over and Moyes decided to bring a lapdog with him to Utd(lots of managers bring a player over with them to have someone they know in the team) who though not good, his position was pretty much attacking midfield as well.
Personally I think the team playing differently(and likely better) could have utilised him effectively whenever they wanted to. Sticking with Rooney, then buying Fellaini and following that up with an expensive and higher wage Mata pretty much sealed Kagawa's fate.
If there was one player out of Mata/Kagawa to get rid of financially there was only one answer, and only one player teams actually wanted to buy.
Good players leave teams all the time for reasons other than quality.
Utd had too many, frankly crap players, playing a completely different type of football to Kagawa. Young, Valencia, Carrick, Fellaini, Rooney. This isn't a team of brilliant interplay, masterful passing, epic movement. It suits neither Kagawa or Mata.
Thing is LVG will likely attempt to get them playing better football, largely through buying better players who would link up well with Kagawa, but financially speaking he had to go because there weren't any buyers for a £35mil lazy Mata who is on the wages he was on.