It seems to me that even if Man U remain unchanged next season, their game shouldn't get any worse... As far as I know, the main players are not leaving the club yet... Man U showed good football last season and finished the season in third place... If they don't have any major team changes, they can continue to play well without any new transfers...
Their problem is similar like Arsenal where they don't have a good player in bench, if there's a player in Manchester United is injured, their performance would be bad. However Manchester United make a crucial move where they let De Gea to leave, goalkeeper is one of the most important position similar like a central midfielder. I don't think Manchester United's performance would be same, it's either they're better or worse.
Not only goalkeepers and midfielders are important in football, because of course all players on every line are important to be able to play well. Also, De Gea is not the only source of Manchester United's problems, because previously Manchester United also had problems in defense or with their defenders. So yes, even though De Gea can play well, but their defenders are very weak, so of course it is difficult for Manchester United's goal to keep clean sheets.