Levein now finds himself under immense pressure as Scotland boss, but the Manchester United midfielder is adamant that 47-year-old can turn the side's fortunes around.
Asked if Levein still has a future with the team, Fletcher told BBC Sport: "I hope so, yes. I really hope so. The players believe in him.
"Qualifying from this group now looks very difficult but we can still progress as a team.
"We tried to win the game. It was always going to be difficult. If we did [attack] we would have lost five or six, trust me."
Scotland's next match in the group is a trip to Serbia in March.