The Cherries chairman is urging fans to keep the faith and raise the roof as Lee Bradbury's side bid to get their promotion push back on track.
Cherries' chances of earning a place in next season's Championship have been hit by three consecutive defeats, the latest reverse coming at Carlisle on Saturday.
The 1-0 loss at Brunton Park saw some of the club's doubters re-emerge but Mitchell insists now is the time to show support, with just nine games of the season remaining.
Bradbury's men have an ideal opportunity to halt their slump when they host an out-of-sorts Charlton Athletic on Saturday. The Addicks have failed to register a win in their past eight matches.
Mitchell is desperate for Cherries to maintain their place in the play-off mix and he believes supporters have an important part to play.
He told the Echo: I felt we lacked our 12th man at the Southampton game but now we need him, wherever he is.
These boys need a lift. They need a lift from the home crowd and this weekend is a home game.
You can't rely on just one end to sing. We have got to let our inhibitions go and join in with the North Stand.
There have been 7,000-plus tickets sold for the Charlton game and we want to hear them. I don't think it will be a sell-out but it won't be far off if all goes well.
We need it now we desperately need this last push. It is not just about the players on the pitch.
One of the favourites for relegation prior to the season, Cherries have defied those odds to put themselves in with a big chance of sealing a place in English football's second tier.
Despite the departures of Brett Pitman, Josh McQuoid and Marvin Bartley, Cherries have remained in the mix, with Bradbury continuing where Eddie Howe left off by claiming 22 points from 13 games in charge.
Mitchell added: Every home game now has got to be a big occasion.
These boys are on the verge of doing what has only ever been done once in the club's history and it is a big occasion.
Look how far we have come with the boys we have got and the board we have got.
We don't want to miss this opportunity. We haven't got a second to lose and we have got to lift our boys and give them some support.