The Deadpool actor, 49, is a co-owner of the Welsh football club alongside It's Always Sunny In Philadelphia star Rob Mac, after the Hollywood pair bought the club in 2021.
On Saturday, the club managed a 2-2 draw against Middlesborough, meaning the Welsh side missed out on the Championship play-offs.
In a post shared on Instagram after the match, Reynolds said: "I am completely gutted by today's result but incredibly proud of our season".
"We've come a long way in five years and this was the best result in our 150-plus year history," he said.
"More to do. But for now, we have so much to be proud of, Reds."
Under their ownership, the Red Dragons shot through the English football ranks, starting out in the National League, the fifth tier and making it through to the Championship, one level below the Premier League.
Wrexham were in sixth place before the weekend but the draw, combined with Hull's win over Norwich, meant they finished the season in seventh and outside the play-off spots.
The Hollywood co-owners have documented the stories of players and staff at the club, as well as people in the wider Wrexham community, in their FX docuseries Welcome To Wrexham.
The show has gone on to win 10 Emmy Awards and two Critics' Choice Television Awards, with Disney+ unveiling the official trailer on Tuesday for its upcoming fifth series.
Season five chronicles Wrexham's quest to reach the top tier of English football and a new-look squad constructed in the summer of 2025.
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