United won just two of their final 12 games of the season to miss out on Champions League qualification and finish 32 points adrift of Premier League champions Manchester City in sixth.
The nadir came in a 2-0 home defeat to relegated Cardiff on the final day of the season, leaving the futures of many of the United squad open to question this summer.
Solskjaer was only confirmed as United's new manager on a permanent basis just over six weeks ago, but that decision has also been questioned given the Norwegian's lack of coaching experience at the top echelons of the game.
However, Solskjaer will not rejig his coaching staff with Michael Carrick, Kieran McKenna and Mark Dempsey continuing alongside assistant manager Mike Phelan.
"They are all going to stay," Solskjaer told United's official app.
"I think that's important, that we keep that team going forward. We do bounce off each other and they are some excellent coaches."
United's clearout has already begun with former captain Antonio Valencia and Ander Herrera leaving the club after their contracts expired.
Spanish midfielder Herrera is expected to join French champions Paris Saint-Germain, but believes Solskjaer's human qualities make him the right man to turn United's fortunes around.
"When you have the players behind you and wanting to fight for you, part of the job is done," said Herrera.
"I believe in karma and if you are a good person, if you are honest and sincere with the players and the fans, sooner or later it will work.
"I think Ole is the right person because he has qualities and knowledge but also he is a great man and a great person."
United have now gone six years without winning the Premier League title since Alex Ferguson retired and Solskjaer admitted it would be "miraculous" for the Red Devils to be challenging Manchester City and Liverpool next season.
But Herrera called for Solskjaer to be given the time needed to get United back on their feet.
"They (the coaches) need time because this is not going to be from the first day. The club will need time, confidence and support," he added
"I am sure they will give it but the only thing I ask for them is time because this is not easy.
"(But) the right person is at the wheel. He's the right person."