Adam Lallana scored his first international goal in the 95th minute of the Group F qualifier in new manager Sam Allardyce's first game in charge.
"Too much is getting made about it. Listen, I'm playing on the pitch for England. I'm captain of the team and I feel I can do a very good job in the role I played tonight," Rooney told Sky Sports.
"It's headlines for a lot of people, but of course it's about the team and about us winning. I played in that role and helped us win the game. I've done it my whole career and suddenly it's big news."
"It's not a big thing and I think there's a big over-reaction to it. I am happy where I'm playing and I think I'm doing a good job."
Meanwhile, midfielder Eric Dier says England will take some time to recover from their Euro 2016 humiliation despite getting back to winning ways in Trnava.
"There is a long way to go until the scars have been healed but it is a start. All we can do is win against whoever we have in front of us but I think there is a long way to go before we repay everyone for what happened in the Euros," Dier said.
"And for ourselves as well because we were the most unhappy of everyone and there is a long way to go until we are happy again."
(Reporting by Ian Rodricks in Bengaluru; editing by Clare Lovell)
