The French midfielder arrived at Old Trafford from Southampton last summer in a deal thought to be worth around £25m.
He has not always been a regular in Louis van Gaal's starting lineup this term, but Schneiderlin stressed that his development in a United shirt has been pleasing.
"When I first came I had big expectations and, of course, I wanted to play for the title and I wanted to have a big impact straight away on everything. It's a new philosophy and a new thing to take on board," he told MUTV.
"I had some good games and a good spell but there's a lot of competition and so even in my time when I didn't play every game I was still learning, still trying to improve and doing my best.
"Since the weeks went on in the season I've felt better and better and of course I know I have plenty more to show to everyone and plenty more in my locker."
The 26-year-old has made 31 appearances in all competitions this term.