Erik ten Hag conceded there are "issues" with Manchester United's playing style amid renewed scrutiny over David de Gea's role.
De Gea was beaten by Ilkay Gundogan's saveable shot that restored Manchester City's lead and eventually secured a 2-1 victory in the FA Cup final.
United are expected to finalise a new contract for De Gea, 32, however their run-in was littered with mistakes by the Spaniard that cost United in the Europa League defeat by Sevilla and loss at West Ham.
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De Gea received the Golden Glove award for most clean sheets in the Premier League but figures at United are unconvinced by his No.1 status beyond this season.
"In this moment, I don't want to talk about such issues of criticism because we all played a great season - including David de Gea," Ten Hag said. "He played a fantastic season.
"If you consider that City, before today, both [teams had] 42 wins and now they have one win more. So the difference was made today and you can tell we played a fantastic season and that is more than we could have expected than before.
"We were third in the league, we qualified for the Champions League, we won a trophy and we were in another final, so I am really happy with the performance of my team all over."
When Ten Hag was pressed on De Gea's problematic distribution, he replied: "Say it like this: we are in the right direction. But there are occasions in the game, issues in the game, we have to improve, definitely, if we want to make the next step and win trophies."
Ten Hag described both of Gundogan's goals as "soft". The German struck the fastest goal in an FA Cup final with a 12-second opener after two aerial duels from Stefan Ortega's hoik.
Gundogan's second came direct from a Kevin de Bruyne free-kick by the touchline. "We win together, we lose together," Ten Hag reiterated. "There were two moments, there were dead balls - one at kick-off and one from a wide free-kick. They can't be a goal. We have to be better organised there.
"As a team, we didn't do the jobs we had to do. And if you want to win trophies, details in big games make the difference and it's hard to accept but we have to."
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