The Switzerland international set up Eric Maxim Choupo-Moting's second goal in Stoke City's 2-2 Premier League draw with United on Saturday, a result that ended the Red Devils' winning start to the campaign.
Shaqiri's former club Basel visit Old Trafford for their opening Champions League group game as clear underdogs, especially since their 2-1 home defeat to Lausanne at the weekend left them without a win in three games.
But the 25-year-old has urged Raphael Wicky's side to be brave and try to exploit United's weaknesses at the back.
"You have to play bravely," he told Blick. "It doesn't matter if you're setting up to sit deep for 90 minutes. They have so much class in attack, sometimes they'll just shoot and score a goal.
"If they do [have a weakness], it's in their defence. That's what our goals have shown. If you play fast and bravely, the defenders have problems. At the back, Manchester are vulnerable.
"It will be extremely difficult for Basel. Especially at Old Trafford, where Manchester are far more dominant than away. Then there's the atmosphere there. Old Trafford is one of the best stadiums in the world.
"Raphael Wicky has to be brave, to risk something. Just defending won't be enough. But he probably knows that himself."
Shaqiri says Basel could target midfielder Paul Pogba, who he says has a tendency to keep possession for too long, although he warned that trying to take the ball from the France star or Romelu Lukaku can be extremely tough.
"You can hardly get him off the ball," he said of Pogba. "However, he sometimes tends to hold on to it for too long. Physically, he's very strong.
"He [Lukaku] also has a lot of power and can really assert himself. You can play it in quickly, to his feet or his chest, or in behind."
Stoke's second goal came from a corner that followed a stunning save from David de Gea to deny Jese Rodriguez.
Shaqiri admits the Spain goalkeeper is one of the best in his position but identified a weakness in his game, too.
"De Gea is an absolutely world-class goalkeeper," he said. "Extremely strong on his line, good with the ball at his feet. Very relaxed, maybe even too relaxed."