The bassist, who left the group in 1992, reunited with his former bandmates onstage for their 50th anniversary concerts at London's O2 Arena in November (12), but he wasn't part of the line-up when the musicians later took their shows Stateside.
Wyman has now revealed he was disappointed to have only been asked to play two songs with the band during each concert, and refused an offer to go to America with them.
He tells the Daily Express newspaper, "It was great for five minutes because that's about as long as they let me play. I thought I was going to get quite heavily involved because I was led to believe that throughout the year by them.
"Keith (Richards) in particular made me think that I would be a large part of it (the reunion) but when it came to it they told me they only wanted me to do two songs. It was fun but I regretted not playing more...
"I came off just as I was warming up and getting into it. When they asked me to go to America for two weeks to do three shows there, I said for two songs? No thank you."
Wyman also insists he now has "better things" to do with his time than hit the road, adding, "I'd say 'no' (to a permanent reunion). Thirty years was great but I've got better things to be doing now. That time has gone."
The Rolling Stones will kick off their 50 & Counting Tour in California in May (13) before heading to the U.K. for a performance at Glastonbury Festival and a show in London's Hyde Park.