The former Dundee coach has come under pressure after the Scots relinquished a 1-0 lead over Chris Coleman's Wales, and ended up losing the game in the final 10 minutes courtesy of two Gareth Bale goals.
Levein's men will now travel to Brussels to face the group leaders, and Fletcher believes he and his team-mates are fully prepared to earn all three points and repay the faith placed in them by the manager.
"We are desperate for the performance and the win for the manager because we believe in him as a team, as a group," Fletcher told Sky Sports.
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"It's a really good set-up to be involved in and all the players genuinely enjoy being here. He treats us like adults, with respect.
"We are allowed to voice our opinions but he has the final decision and everyone respects him for that. Hopefully we can get a much-needed victory.
"The players are fully behind the manager. I don't think we could be better prepared for matches than we are. I honestly believe that.
"The manager has come in and had a really positive impact on the whole structure at the SFA.
"He has definitely had a positive impact on the squad.
"We've had some good performances and we just need the results and hopefully they come sooner rather than later."