The Norwegian departed following Saturday’s 4-1 defeat at Watford and spoke to the players at Carrington before leaving for the final time.
Michael Carrick has been placed in temporary charge of the team and he appeared at a press conference on Monday alongside Maguire to preview the upcoming Champions League clash with Villarreal.
And Maguire admitted that he was disappointed that the journey with Solskjaer was on had to come to an end after the loss at Vicarage Road.
"Well, like Michael’s said, I think it’s been a very hard time for us as players as well because of the amount of respect we have for the boss and what he’s done for a lot of us over the two-and-a-half-year period he’s been here,” Maguire told journalists.