Almost 10,000 fans turned out to watch the Gills see off Rochdale in their play-off semi-final second leg, and Stimson - who was unable to save the Gills from the drop last season - believes that shows the potential of the Kent outfit.
He said: "This club is geared for League One, if not better, but it's getting there first. The fan base is absolutely huge, you've seen that.
"I hope they all save up and get themselves down to Wembley because it's a fantastic stadium and the more Gillingham supporters, the more noise, the more chance we've got of winning."
The Gills will now face Shrewsbury - who beat them 7-0 back in September - at Wembley on May 23 and Stimson believes the showpiece final is a just reward for his hard-working players.
"I'm very happy for the players," he added. "The majority of them came back on the first of June - some of them weren't too happy because I cancelled a lot of their holidays, but you get your rewards if you're prepared to do that little bit more."