The England striker was pivotal in the Red Devils' comfortable victory against West Brom on Saturday lunch-time, which he believes will set them up for difficult fixtures in March
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Rooney scored the second goal and laid on the third for Danny Welbeck after Phil Jones had given David Moyes' men an early lead.
Moyes has been under pressure since United lost 2-0 to Olympiakos in the Champions League, but Rooney says it is now up to the players to fight for the club.
"We were hurt after the Olympiakos game, of course we were, we wanted to come and show everyone we're a good team and fight for the shirt and for our place in the team," he told BT Sport. "I think that showed today, we played with great energy and we were exciting and we always looked a threat.
"The 3-0 win was deserved and maybe it could have been more."
The Red Devils welcome Liverpool to Old Trafford next Sunday before hosting Olympiakos and Manchester City before the end of March, and Rooney says it is a perfect opportunity to remind the rest of the Premier League of the club's quality.
"Liverpool next and then Olympiakos, where we're two goals down, then West Ham away and City," he added. "It's a big challenge for us and it's up to us to us to take that challenge, show everybody we're a good team and that we mean business."
Michael Carrick was also pleased with his team-mates' performance on Saturday, particularly when going forward.
"It was all about the result today," he said. "We were ready for today, we knew it was important, but the performance was exciting, we looked good going forward.
"We looked promising at times, it's up to us to perform. We've got the players to do it, and when it comes together we look good. It's up to us to do it again."