The striker, under scrutiny after a poor start to the season, scored a hat-trick in the 4-0 win over Club Brugge in the Champions League qualifier.
"If I didn't have a strong character, that may have affected me, but I know my quality," 29-year-old Rooney said.
"If the goals don't go in I still bring a lot to my team-mates."
Victory secured United's place in the Champions League group stage following a one-season absence.
England captain Rooney has been playing as United's main striker this season but had not scored in the side's opening four games in all competitions.
He went into the match in Brugge with his most recent United goal having come against Aston Villa in April, but he ended his 878-minute club scoring drought in emphatic manner.
His first was a dink over goalkeeper Sinan Bolat before he side-footed in and then swept home a shot, while Ander Herrera grabbed United's fourth.
"I wasn't worried. If it was going on for three, four, five games more then maybe, but it's early days and I knew when the chances came I'd take them," Rooney told BT Sport.
"Everybody goes back to last season and it was so many games without scoring, but a lot of top quality strikers are yet to get off the mark at this stage.
"I understand because of my name and because of who I am it will get publicised a lot more. That's my job and I understand that."
Manchester United manager Louis van Gaal said: "It has given him always the confidence that a player needs.
"Wayne has a very strong mentality and with his level he shall always come back and he proved that."
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