Matic spent United's first three matches of the season sat on the bench, while in their 1-1 draw with Southampton he came on only for the final 22 minutes.
Per Goal's Sacha Pisani, Matic said:
"In the first two or three games he determined the team without me.
"I work as hard as I can, we respect the decision, it is mine to show him that he was wrong and to bring me back to where I belong.
"There is no problem. I told him I disagreed with him, but that he had to decide the team."
The Serb added that Solskjaer picks the team, and as such he "bears the responsibility" if his selection does not win games.
Matic arrived from Chelsea in 2017. He was a valuable player for the Blues, for whom he made 154 appearances, because of the steel he added to their spine and the protection he offered the back four.
The midfielder only turned 31 in August, but he appears to have declined physically since his move to Old Trafford.
He failed to impress in pre-season, and football writers Liam Canning and Jordan Clarke were critical of him in United's final friendly against AC Milan, in which the Rossoneri scored after he was caught in possession:
Matic no longer possesses the mobility required in his role. He slows the Red Devils down when he's in possession, and he struggles to keep up off the ball.
Football author Collin Millar questioned the decision to bring him on against Southampton in United's most recent game:
Matic is a reminder that while the likes of Aaron Wan-Bissaka, Harry Maguire and Daniel James were promising signings, United's recruitment this summer failed to address what should have been a priority.
With Marouane Fellaini moved on in the winter and Ander Herrera also leaving this summer, the club were in desperate need of at least one central midfielder.
Solskjaer has shown he can't rely on Matic or Fred, who hasn't even made the bench this season and last featured in April.
Given Andreas Pereira, Juan Mata and Jesse Lingard tend to play further forward or in a wide position, Solskjaer has few options in the centre beyond his first-choice pairing of Paul Pogba and Scott McTominay.
Matic will pick up more game time this season as a result of those limitations, but unless he can significantly improve they can ill afford for him to play a key role.