Rooney’s place in the side has been a subject of debate and he made amends for missing a close-range chance by heading United’s second goal.
“I’ve got nothing to prove to anyone,” Rooney told Media: “I’ve played this game a long time. I believe in my ability. If I play the way I played today, I’ll score goals.”
Rooney is in positive mood after a summer in which United have spent big in the transfer market, with Paul Pogba still to make his debut after he was suspended for Sunday’s opener.
“We’ve made a real statement this season,” he added. “We’ve made four great signings who’ll improve our team. The new manager is a successful manager. There’s a lot of excitement.”
Earlier, Juan Mata had scored the first Premier League goal under new manager Jose Mourinho, before league debutant Zlatan Ibrahimovic added another goal to put the game beyond doubt.
Ibrahimovic has now scored on his Premier League, Serie A, La Liga, Ligue 1 and Champions League debuts. The Swede said: “It was not easy. Everything is new to me. Slowly, I’m getting settled in and just playing my game. For me, the winning is the most important and whoever scores is a bonus.”
Discussing the team’s performance, he added: ” In the first half, we weren’t 100 percent but, in the second half, we became better.”
The afternoon’s work satisfied Mourinho, who told Media: “I am very happy. Bournemouth always start with great intensity but we kept our control. We weren’t surprised and then we started playing. In the second half, we had a bit more confidence.”