Allardyce lauds Everton's 'masterful' Rooney
The hosts were wasteful in the first half at Goodison Park, but Gaetan Bong's own goal – forced when Theo Walcott sought to get on the end of Yannick Bolasie's teasing delivery – broke the deadlock on the hour mark.
Rooney played in a deep-lying role and enjoyed plenty of time on the ball, with Cenk Tosun doubling the Toffees' lead before the former England international saw his spot-kick saved by Mat Ryan.
It did little to diminish Allardyce's view of Rooney's overall contribution, with the 63-year-old singing his praises.
"What a masterful job he did for me," Allardyce told the club's official website. "His passes were the reason we were so fluid I felt in the fist half and then again the second half.
"I think the only thing that let us down first half was our quality in front of goal, that improved second half brilliantly with three instances, particularly the first goal, which was an own goal, which was unfortunate Theo didn't score it.
"The second goal was a nice little lay-off to Cenk and a beautiful finish and then the skill into the box from Dominic [Calvert-Lewin] to get the penalty – I don't think anybody's got any doubt about that, it's a brilliant piece of skill to get around the defender in that tight situation.
"It's just a shame Wayne didn't finish off what would have been an outstanding performance. I suppose missing it at this level when you're 2-0 up it's not so bad, so it was still an ousttanding performance, but that would have been the crowning glory for him."
FT. Clean sheet + two goals = three points. #EFCmatchday pic.twitter.com/o8PwjRNAWO
— Everton (@Everton) March 10, 2018
The visitors were reduced to 10 men late on following a straight red card for Anthony Knockaert, who dived in two-footed on the returning Leighton Baines, and boss Chris Hughton offered no defence of his player and expressed surprise at his side's lacklustre showing.
"I've not spoken to Anthony. Of course I will, but I've got no complaints," said Hughton.
"I was surprised, particularly with the form we've been in. You can't come to Everton, who have been very good at home, and play at a level that doesn't allow you to get anything from the game.
"At half-time, having not played well, we were still very much in the game. For all the corners that they had and ball in that final third, they never really had clear chances.
"There was an opportunity for us to come out better and improve in the second half and unfortunately we didn't."
The result lifted Everton up to ninth, while Brighton – who sit 11th – still have some work to do to pull away from relegation trouble.