The former Manchester United and England captain was appointed by the second-tier club in May.
Rooney previously lasted just three months in charge at Birmingham, sacked in January just 83 days into a tenure in which he oversaw nine defeats in 15 games.
Birmingham had been sixth in the Championship at the time of Rooney's appointment but they ended the campaign getting relegated.
The former forward, who has previously managed at Derby and DC United in the United States, intends to put that experience behind him.
"You always have to prove yourself," he said. "I think that's what I had for 20 years as a player and, as a coach, wherever you are, whatever job you're in, you have to prove yourself. That's normal, that's a pressure which comes with the job.
"And of course, when you go into jobs, you leave yourself open. If you don't get results, then obviously there's consequences to that, which was the case at Birmingham."
Rooney, 38, said he was excited to start work at Plymouth, who narrowly escaped relegation to the third tier last season in their first campaign back in the Championship.
"I took a lot of time to reflect on what happened at Birmingham," he said. "Sometimes things happen for a reason. The good thing which came out of it means that I'm here now, and I'm here to go and be successful. I really believe in that.
"I'm a confident person and I back myself to do that. I'm just looking forward to getting started."
Rooney succeeds Ian Foster, who was sacked in April with Plymouth in relegation danger.
Argyle went on to survive on the final day of the season, with Birmingham dropping to League One instead.
Rooney hopes to take the club to the Premier League but admits it is a longer-term ambition.
"Of course I'm not going to come out and say we're looking to get Premier League in a year's time," he said.
"We think we need to be realistic and what we're trying to do is build on where the club has been over the last five years, which has been rising and getting better over time."
