The Potters slipped up at Sunderland last weekend, losing 4-0 after remaining undefeated in nine matches (in all competitions) to start the season.
Despite the loss at Sunderland, Shawcross says Stoke has the ability to test the peerless United who sit atop the Premier League table with a perfect record from five games.
"It was probably a bit of a reality check for us to be honest, especially having been on a nine-game unbeaten run to start the new season," he said in Stoke's official matchday programme.
"Good runs have to come to an end, but it was disappointing for it to end in that fashion at Sunderland. The result and the performance were disappointing, but we move on now and we set our sights on another unbeaten run like the one we have just had.
"It will be hard to start that off against Manchester United because they are a top team, but everyone is beatable, and we know if we have the fans right behind us and we perform in a way we know we can, then we do have a chance."