Welbeck pounced on Antonio Valencia's under-hit back pass, rounded David de Gea and netted to give Arsenal a 2-1 win and a place in the semi-finals.
The England international joined Arsenal on deadline day in September last year and said it was tough to face United at Old Trafford.
"It was a great reception," Welbeck told arsenal.com.
"It was hard for me but I tried to be respectful."
Much was made of Welbeck's decision to celebrate after he scored the winner in the 61st minute.
But the 24-year-old said he was just happy to have helped Arsenal into the last four.
"It was about being professional, keeping my focus and motivation," Welbeck said.
"I kept plugging away and then got on the end of Antonio Valencia's back pass, beat David de Gea and got the winning goal.
"I'm just really pleased we're through to the next round."
