Experience is important, but it isn't the end all, be all IMO. I have noticed in the past my players would play better and had decent amounts of experience.
The quickness with which experience is earned depends on the type of game (Scrimmage, League, Playoffs, Cup, etc.) and how many minutes a player plays. The more you play a player, the faster they will get more experience.
I can't remember which type of game gives the most experience, but I'm pretty sure scrimmages give the least. Also, I think Private League games don't count.