Martial scored 24 goals in all competitions and finished the campaign as United's top goalscorer.
The France international also made more appearances than the previous season and praised Solskjaer for giving him more minutes than his predecessor Jose Mourinho.
"I think it's down to the fact that I've enjoyed more game time," he told the Inside United magazine. "I've played in practically every game and so I think it's all about consistency.
"In previous seasons I haven't been able to feature as regularly; I'd be on the bench quite a bit and other times I'd be starting, which was quite difficult. Whereas right now I know that the coach has faith in me and I'm confident of starting the next match. So, I'm giving everything I can in order to pay back that trust he has shown.
"[I'm hungry for all goals] because for me, a goal is a goal. So simply by managing to score more of a simple kind of goal, I know that I'll score a lot more in total. It's something that we work on a lot in training and I then try and reproduce that in a match situation."
Under Mourinho, Martial was not a regular starter and said he was determined to prove his former boss wrong during his time at Old Trafford.
Martial scored one more goal than teammate Marcus Rashford but said there is a "healthy" relationship between the two forwards.
"With Marcus, I think that we've been playing together for five seasons now and so, yes, we have that good understanding. It's a real positive for us that we have this great connection," Martial added.
"We just try to help each other out. For example, there are some games where maybe a shot is on and then I decide to wait and see, and I give him the ball because I want him to score. And he does the same thing for me, so you see, we're not just focused on scoring all the time.
"We're always going to do everything we can for the team to win which means that, if he is better placed than me or I'm in a better position than him, we'll always give each other the ball in order to score.
"There is healthy competition, but the biggest thing is the positive rapport that we have with one another."
United will begin their Premier League campaign with a home match against Crystal Palace on Sept. 19.