Goals from Chris Smalling, Wayne Rooney and Robin van Persie condemned Bruce's men to a fourth consecutive Premier League defeat.
Hull are without a win in the top flight since beating Crystal Palace 2-0 in early October, and Bruce's side rarely looking like ending that run at Old Trafford.
While a listless performance left Bruce frustrated on his 700th game in management, the former United captain was also unhappy with sloppy errors that led to some of his former club's goals.
"It was a very difficult afternoon for us, there's no mistaking that," Bruce explained.
"I think the disappointing thing for me was the mistakes. I know Manchester United were good on the day but the mistakes we made - you can't make mistakes in the Premier League that we've made today.
"It was difficult enough for us but the way we gifted goals to them, you can't do that at a place like this."
Despite Hull's woeful run of form, which leaves them 17th in the table, Bruce maintains his side can finish higher than their 16th-place effort last term.
"We knew it was going to be difficult second season in, we did very decent last year but I'm convinced with the squad we've got that we'll finish above where we did last year," he added.
"We knew the opening seven or eight games away from home were going to be difficult, we've been to Arsenal, Liverpool, Newcastle and now we've been here.
"We always knew that the first half of the season away from home was going to be difficult but then again we're Hull and there's a reality about us that we knew there were going to be difficult moments.
"We've got to see it through and see if we can put some results together."
