The result means that Louis van Gaal's side failed to bridge the 10-point gap between themselves and Chelsea, but Shaw insists that his teammates have plenty of time to catch them.
"Of course we are still in the title race," he told Sky Sports News. "It's a long season and we are at the start of it. You don't know what will happen during the middle of the season.
"We know we have still got the best to come. I don't think we are playing our best at the moment and sometimes you saw that against Chelsea.
"It will take time but when we are all on form I think we are going to be a scary team to face."
The Red Devils face local rivals Manchester City at the Etihad Stadium on Sunday afternoon.