Villa slumped back into the drop zone on Saturday after suffering a 2-1 defeat away at Arsenal.
Paul Lambert's side have now won just one of their last 10 top-flight fixtures to remain firmly entrenched in a basement battle.
The struggles of others are helping to keep their survival hopes alive, though, with only goal difference keeping them inside the bottom three.
Weimann, who found the target at the Emirates over the weekend but concedes he was at fault for Arsenal's late winner, is confident Villa can haul themselves clear of trouble if they continue to believe in themselves.
He said: "We're all confident we can get out of this.
"It's never nice to concede at the end but we to take belief from the way we played.
"It was me who let the left-back (Nacho Monreal) in behind me. I switched off. But we're confident of turning it around.
"I should have tracked him. I tracked him all game and for one second I switched off."