كتب : Ahmad Saied
The Black Stars were one down before Michael Essien and Junior Agogo found the net to lift Ghana to the semis on Sunday.
"They helped us a lot, it was fantastic," Muntari told BBC Sport.
Supporters packing the Ohene Djan stadium in Accra were silenced by the opener but started to roar the team on after the equalizer.
They kept chanting after captain John Mensah was sent-off before erupting in ecstasy as Agogo scored the winner eight minutes from time.
"You can't describe it, we thank them for coming and cheering us, and we'll try our best not to let them down," Muntari added.
In the group stage, Muntari's teammate Asamoah Gyan threatened to walk away from the tournament in protest over fans' behavior.
Sections of the crowds booed him during the first two games after missing easy chances despite his pleas for support.