The 22-year-old striker opened the scoring for the Reds in Spain and, although Cristiano Ronaldo quickly levelled matters, United gave as good as they got in securing a 1-1 Champions League draw.
"You come to the Bernabeu and it's a magnificent stadium," Welbeck told Sky Sports. "With all the names they've got we just knew we had to set out as if it was going to be another game.
"We came here to play the game, not the occasion, and no matter who we're playing against we're going to set out like Manchester United do and try to win the game."
Welbeck admitted his well-taken header from a Wayne Rooney corner was the result of well-rehearsed set-piece routines, saying: "Once Wazza took the corner, I knew exactly where he was going to put it. We've got different routines, and thankfully it came to me and I stuck it in the back of the net."
Shortly before half-time, he came agonisingly close to doubling his haul, only for Real shot-stopper Diego Lopez to turn away his prodded effort from a Robin van Persie cross.
"It was very close," he added. "It was a great ball by Robin, it was just inches away. Just a step forward and maybe I could have stuck it in the back of the net, but it was just a bit too far."