The striker says it has been tough to watch the Red Devils' rivals outperform them this season, and also admitted that he would like to take over the captaincy from Nemanja Vidic
The reigning champions have not been involved in the title race this season and are even outsiders for a place in the top four.
Chelsea are currently seven points clear at the top of the table, but both Liverpool and Arsenal have one game in hand, while City have three, and Rooney says it is especially hard to have to sit back and watch United's traditional rivals battling for the top honours.
"To see City doing well, and particularly Liverpool, is really difficult," the England international told club magazine Inside United.
"It's not nice when we know we are capable of being up there challenging and we haven't been doing that this season.
"However, it means we have to step up and get back up there because the feeling we've had this season is not a nice feeling at all to have.
"We have to keep working, keep progressing and finish the season stronger.
"As a group of players and a team we haven't been good enough this season and we have to put that right.
"After Sir Alex [Ferguson] being here for 26 years, there was always going to be a change whoever came in and, in fairness, I think the players have to do better."
United skipper Nemanja Vidic will leave Old Trafford for Inter at the end of the season and Rooney has admitted he would like to take the armband for next season.
"I've captained a few times for United and if the manager wants me to be captain, I'd have no problem with that," the forward added.
The England captaincy could also soon be up for grabs, should Liverpool skipper Steven Gerrard elect to call time on his international career after this year's World Cup.
And Rooney, who has captained his country twice in his 89 appearances to date, would also relish the chance to lead England on a full-time basis.
"It'd be a great honour to captain my country but, again, it's the manager's call and I'm sure he'll have a few contenders," he continued.
"You don't know what Steven is going to do in the summer, only he knows."