The Red Devils finished seventh in their first season since legendary manager Sir Alex Ferguson retired and started the Louis van Gaal era with a 2-1 defeat at home by Swansea City on Saturday.
The striker insists that getting one over their critics is not the team's main motivation but is desperate to put the troubles of last term behind them.
"We are not out to prove people wrong," he told the club's official website. "We are out to win things for ourselves, the fans and this club.
"We know last season was a disaster. It wasn't good enough and it's always a bigger story when Manchester United struggle – you are going to get ex-players having their say. We have to accept it and be ready for it.
"We know that, if this club is successful, it is great and, if it is not, then there are a lot of people who are waiting for you to fall so they can get at you.
"We have to make sure we are successful. We have to make sure last season was a one-off because that was not good enough."
Rooney scored United's only goal in their Premier League opener, equalising Ki Sung-Yueng's first-half strike, but Gylfi Sigurdsson wrapped up the points for Garry Monk's side.