Ramsey delivered a string of outstanding displays during the first half of the Premier League season and his recent return from a three-month injury lay-off has coincided with an upturn in Arsenal's fortunes.
The Wales international faced criticism earlier in his career as he struggled to find his best form following a double leg-break in 2010.
Having now blossomed into a key figure for Arsenal, Ramsey acknowledges the significance of the faith shown in him by Wenger.
"The manager had loads of chats with me about it (criticism of his form) and always said: 'Never let it get to you, because I know what you can do'," Ramsey told The Guardian.
"I'm grateful for what he's done for me and for the faith that he's had in me.
"Even when I was injured he gave me a new contract. Through the criticism he played me.
"He's always believed in me and I can't thank him enough for that. I owe a lot to him and hopefully I've delivered some of that back this season."
Arsenal led the Premier League for much of the current campaign, but damaging defeats to title rivals ultimately proved costly as Wenger's side slipped out of contention.
In away losses at Manchester City, Liverpool and Chelsea, Arsenal shipped a staggering 17 goals - yet Ramsey is confident the club can still achieve future success.
"It's hard enough going to those places anyway, never mind the fact that we went one or two goals down early on in the games," he added.
"They were the games that really cost us. You take those three matches away and we've been really solid as a team.
"So that's what we need to build on next season, stay in the games early on in the first half, when maybe we've been a bit naive."
"I believe this team has what it takes to win things.
"I'm happy here, I feel we have a team that can be successful and I want to be part of that."
