United are set to finish fourth in the Premier League, which will earn them a spot in the Champions League playoffs in August.
While United have enjoyed a lot more success this year in comparison to their seventh-place finish last season, Rooney feels that his side have nothing to be proud of as their trophy cabinet remains empty.
"We want to go and win the last game of the season, then next season we really want to push for silverware," Rooney told reporters at the United Player of the Year award event at Old Trafford. "Unfortunately no silverware this season, but I think we're looking forward. We've done what we wanted to do this season.
"The main aim this season was to get back in the Champions League. We've done that and we know we've got the quality in the squad to push on next season."
Rooney is also pleased that United are set to make their Champions League comeback after missing out on the competition last season.
He added that being away from a prestigious tournament for such a long period of time can have detrimental effects on the players and the team as a whole.
To illustrate his point further, he used Liverpool as an example.
"If you look at Liverpool and what happened to them, they were without it for years, which was no shame, but I think one year was far too much for this club," he said. "Our main objective this season was to get back into playing Champions League football and kick on next season. We're establishing a very good squad, who I believe can go on and win silverware next year."