Carroll is currently on a season-long loan at Upton Park from Liverpool, who paid £35million for his services in January last year.
The former Newcastle forward struggled for form at Anfield and has scored only once since moving to West Ham.
The 23-year-old was keeping Cole on the bench when fit but is now sidelined with a knee ligament injury.
Cole has replaced Carroll in the side and performed well since with the ex-Chelsea striker believing he has developed into a well-educated front man.
Carroll has nine England caps but Cole reckons he is still learning and will continue to improve in the coming years.
"With Andy he's a brilliant player, I knew he was a brilliant player before he came here," he said.
"He just needs the right break and once he gets going - I know he's only 23 at the moment - but the funny thing about the striker role, or the one we play, is that it takes a long time to learn.
"For Andy to have that skill so young is a real blessing for him because I had to mould myself into that player.
"But he has it naturally, so he just needs to get a few more games. You'll see the best of Andy Carroll when he's 29 or 30, but right now he's still learning his trade."
Cole himself is now 29 and does not think he has finished his footballing education, despite making his first-team debut for Chelsea over 11 years ago.
"You start to learn the game a little bit more, situate yourself in parts of the pitch where you need to be, and impose yourself on certain players that you need to impose yourself on," he said.
"That's what I've learned. I'm still learning. It doesn't happen overnight.
"Andy's going to learn how to impose himself in the proper way.
"I'm not saying I'm better than him or he's better than me but you've still got to learn your trade. He's got great assets. I've got good assets but you've got to know how to use it as well."
Cole could have left West Ham when they were relegated at the end of the 2010/11 season but took a pay-cut to stay at Upton Park and helped the club secure an immediate return to the top flight.
Carroll came into the club with a massive reputation to accompany the high price tag at the start of the current season but Cole believes in his own ability.
He said: "You need someone to push you and obviously Andy Carroll is a fantastic player and I need to show what I could do as well and he's doing the same thing showing what he can do and now I'm pushing him.
"People just think it's one-sided, it's not just one-sided; in training I'm doing what I have to do, he's doing what he has to do and although he might get the first pick, it doesn't matter - in training we're trying to improve ourselves and it does pay off."