Glasgow reached their best-ever league finish of second before losing out to the Irishmen in the play-off final in Dublin, but Stuart believes the squad can take great confidence from their steady improvement in recent years.
Speaking to glasgowwarriors.org, Stuart said: "Next season we've just got to do the same as last year. We targeted being the first Scottish team to win the league and I believe next season will be no different.
"Over the last three seasons we've been improving every week and we're in a good place just now.
"I believe the boys have been working incredibly hard during pre-season training and it all starts from there and hopefully we can go one better and win the title next season."
Head coach Gregor Townsend has brought in five new players to Scotstoun as he seeks to improve his squad ahead of their opening day clash with Munster on the first weekend of September.
Among those players is James Downey and Stuart is excited about the prospect of lining up alongside the former Munster centre.
"It's always good to get new faces into the club and new friends and at the end of the day it's another player in the team who can add something and I'm excited to see what they can offer," he said.
"I've had a few nightmares in the past playing against James (Downey) with him running down my channel, so it'll be good to play off him. He's a strong ball carrier and it's exciting to have the chance to play with him next season."