Shaw has been encouraged by the team's performance in the 1-1 draw against leaders Chelsea though, and he believes he and his team-mates are still playing below their potential.
"Of course we are still in the title race," the United defender said.
"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 just have to keep winning the games coming up. There will be tough games but we know we are good enough to win them.
"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."
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