Barca will take a 1-0 lead to Camp Nou thanks to their midweek success at Old Trafford, where a Luke Shaw own goal put the LaLiga giants in the box seat in the quarter-final showdown.
It was Barca's first European victory away to United, though Pique warned against complacency after what happened to PSG, who won 2-0 in Manchester before capitulating 3-1 at home to bow out on away goals in the last 16.
"After seeing what they did against PSG there's no reason at all to believe the tie is over," Pique told reporters.
"PSG were the clear favourites then, they played far better and look what happened.
"Anything can happen in football, so we'll have to focus very hard."
After opening the scoring in the 12th minute, Barca seemed happy to hold onto their lead as United pushed forward in search of an equaliser.
However, Barca were strong defensively, with former United centre-back Pique immense against his old club.
Pique added: "We put in an excellent performance defensively, we're in our best form in defence of the season.
"The early goal relaxed us and we knew how to cope with the situation, the fact we didn’t concede helps us a lot.
"It's very difficult to come here, it's an historical ground, there's a sensational atmosphere and you get put under a lot of pressure."