Despite losing to two Steven Gerrard penalties and a Luis Suarez strike, Old Trafford remained vocal throughout much of the game and the fans notably sang a rousing rendition of '20 times Man United' as the disappointed players left the field at full-time.
Speaking exclusively to MUTV, Rooney explained why his team-mates are determined to repay the fans' backing during Wednesday's make-or-break clash with Olympiacos in the Champions League.
"It's disappointing, but we have to bounce back because we have a big game on Wednesday," Rooney said. "I thought the fans were magnificent. Towards the end, they were fantastic for us. Us, as a team in the dressing room, we really appreciate that. It's difficult but we've been here before and this is where the character of the lads will have to shine through."
Pressed further on the fans, Wayne continued: "They were fantastic. The support they gave us was really great. Under such difficult circumstances, it was probably the best it's been. They stuck behind us until the last minute and, as we were walking off the pitch, they were right behind us. As a group of players, we really appreciate that."
Sunday's defeat to Liverpool leaves United seventh in the Barclays Premier League table and 12 points shy of the Champions League places. Asked if the Reds can still make it into the top four, Rooney was reluctant to dismiss it. "Who knows? It'll be tough. We'll keep going, you never know in football. As long as we're in with a shot, we'll keep going. If it isn't to be, it isn't to be and we'll move on. The most important thing now is to prepare for Wednesday."