Allardyce was forced to resign as England manager after just 67 days and one game in charge following his controversial comments to undercover newspaper reporters investigating football corruption.
Gareth Southgate will server as England's interim boss for the next four matches and one of his first decisions was to retain Manchester United striker Rooney as his captain.
Rooney is set to lead England in Saturday's World Cup qualifier against Malta at Wembley and the 30-year-old is eager to focus on football after a difficult period for the national side.
"We need to build on the three points we won in the last game (against Slovakia), and the other side of it isn't our issue, it's nothing for us to be concerned about," Rooney said on Tuesday. "It's a shame, everyone could see how excited Sam was for the job and he came in and showed that enthusiasm to the players.
Sam Allardyce could face ban: Football Association
The Manchester United captain continued, "As a group of players we need to stick together and concentrate on the football. For the FA I'm sure it has been a tough couple of weeks but for the players we've been with our clubs and we have to focus on the games."
The start of Rooney's England career intersected briefly with the end of Southgate's international days just over a decade ago.
And Rooney backed the temporary appointment of the England Under-21 boss as the ideal solution to a difficult situation.
"When I first got into the squad he was in the squad then. He's done a very job with the Under-21s, and he's got an opportunity to show what he can do at senior level," Rooney added.
England players get postcards from sacked Allardyce
Rooney's role with England has been under heavy scrutiny since his lacklustre displays during a disappointment Euro 2016 campaign.
Relieved that Southgate remains firmly on his side, Rooney hopes to repay his faith against Malta and then Slovenia in another qualifier next Tuesday.
The 30-year-old striker added, "There was a lot of talk over whether I'd be captain or not, so it was good Gareth put that to bed quite early and there wasn't the speculation. We've got two games this week that we have to win. Whether that was with Gareth or Sam we have to try and get six points. If we do that Gareth will be happy and we'll be happy."
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ