Tommy Wright's side are seven games unbeaten in all competitions, one point off third place in the Premiership and in the League Cup semi-finals.
"Obviously we would like to fill the stadium, but we can't do it for whatever reason," Craig, 28, said.
"The chairman has been on record as saying we've not got the biggest support, but they're passionate crowd."
Saints took all three points from Saturday's trip to Dingwall to face Ross County, with Dave Mackay's late free-kick ensuring a 3-2 win despite letting a two-goal lead slip.
"We've got a group of players who have got a lot of trust and belief in what the manager wants us to do," Craig told BBC Radio Scotland's Sportsound.
"We've got a manager who's got a lot of belief, confidence, and he gives his players a freedom to go and express themselves.
"We've got the experience in the team to go to places like County when the conditions weren't great."
Saints' Michael O'Halloran won November's Premiership player of the month award and Craig is hopeful the 24-year-old will stay in Perth until the summer as they compete on three fronts, with the semi-final with Hibernian and a Scottish Cup fourth-round tie against Kilmarnock on the horizon.
"It's great to have him in the team because he gives you an outlet, he's a match-winner," Craig said of fellow Scot O'Halloran.
"He's very important to us, but take nothing away from the rest of the players.
"But you can't give Mikey or the manager enough credit. A lot is being said about him but he's not getting too big for his boots.
"He knows what he's got to do to stay in the team and we're going to hopefully have him until the end of the season at least."
Midfielder Liam Craig hopes St Johnstone's recent form can help attract more fans to McDiarmid Park.