England and Manchester United's all-time leading goalscorer swapped Everton for MLS by signing a three-and-a-half-year deal with DC in June.
The forward struggled for form after returning to his boyhood club Everton in 2017 in a deal that sent Romelu Lukaku to Old Trafford.
However, the 33-year-old helped lead DC from the bottom of the Eastern Conference and into the play-offs, scoring 12 goals and supplying six assists in 21 appearances.
"If I'm being honest, I know quality wise, I can still play in the Premier League," Rooney said.
"I know that. I've always been a confident person, and so I have high expectations of myself.
"I've come here expecting to do well and I think there was a surprise from people who have their opinions, which is fair enough, but I never doubted myself at all."
Rooney was let go from Manchester United by Jose Mourinho, and he reiterated his belief that Mauricio Pochettino should be employed as the Portuguese's replacement.
But he thinks interim boss Ole Gunnar Solskjaer would be a good option if he maintains the form that has seen him go unbeaten in his first 10 matches at the helm, winning nine.
"Ole Gunnar's a fantastic person," said Rooney.
"I think the club will have a decision to make at the end of the season, and it'd be nice to see Ole continue with this form and get a shot at the job on a permanent basis.
"But if not, if the club go to choose someone else, then I think in my opinion Pochettino would be the right guy."