Martial was visibly unhappy when being substituted during the second-half of victory over Aston Villa last night.
But Solskjaer explained, "Anthony's getting fitter and fitter and he could have lasted the game of course and he's starting every game.
"I'd be more worried if he wanted to come off. Everyone wants to be a part of the team, be on the pitch and he's put a shift in so that's fine.
"It's great for me to have him available to start every game."