Athletic's 3-2 victory on the Reds' home patch has put them in the driving seat in the last 16 tie, with United needing to win Thursday's second leg by at least two goals.
While Sir Alex's men have been riding high in the Barclays Premier League of late, the Reds have stuttered in the Europa League after the disappointing exit from the Champions League back in December.
United had to hold on for victory over Ajax in the last round and last week's result at Old Trafford has made the chances of progression to the quarter-finals even tougher. But Rooney maintains the Reds are capable of turning things round.
"We have to be confident," he told ManUtd.com. "They obviously played some great football at Old Trafford and deserved to win.
"We need to show better than what we did that night because we let ourselves down.
"We'll be going out there on Thursday to do our best to win and get through to the next round because this is a competition we want to win.
"It'll be a difficult game but we all have the confidence and belief that we can do it."