The forward branded United's performance in Tuesday's 3-0 defeat to rivals Manchester City as a "bad night" as Moyes' men fell to a sixth home league loss this season.
Old Trafford developed a reputation as a fortress across two decades of Premier League dominance but the defending champions appear to have lost that aura.
Teams are heading to United in the belief that they can win, as evidenced by their recent return of just one point from three home matches, in which they have conceded eight goals.
And Rooney confessed that visiting sides no longer feared facing United on home soil.
"It's not good enough," the England striker told MUTV. "We can't lose six homes games in a season and we have to put that right, and make this a place which teams fear again.
"It's probably been the story of our season so far that we've got a couple of good results and then one which sets us back a bit.
"We know we have to respond. It's a bad night for us all but we have to move on.
"No-one likes to lose a derby game – they're big games and they're great to win, but when you lose it's not a great feeling. For the fans and for us, we have to win more and stay together."
United face Aston Villa at home on Saturday before UEFA Champions League holders, and newly crowned Bundesliga champions, Bayern Munich arrive on Tuesday for their quarter-final tie.
