The 22-year-old defender made his first league start for Villa in Saturday's 3-2 home defeat against Manchester United.
Injuries and suspensions to the likes of Joe Bennett, Eric Lichaj and Nathan Baker presented the Irishman with his opportunity.
Stevens, signed from Shamrock Rovers last January, said: "I'm hoping to keep my place, I've got confidence. I'll go into training and train well and hopefully I'll stay in the team for Manchester City.
"This debut has been a long time coming, but, when you get your chance, you've got to take it. It's a great experience, it brings out the best in you. You know where you stand when you play against the best.
"It's a massive experience but I'm just looking to kick on."