Despite a poor season that has left them in sixth place in the Premier League table, United have picked up more points away from home than any other club in the top flight.
The 4-0 win over at Newcastle United on Saturday was the reigning champions' 10th win on the road, and Moyes has said that the expectation at Old Trafford is what has affected his side's home form this season.
"Maybe there's a big expectation at Old Trafford to go and be a bit gung-ho and play in a real attacking style," the Scot told reporters.
"We've lost a few games by narrow margins - 1-0 (to) Newcastle United, Everton. We've lost a few games like that, whereas maybe away from home there's not as much expectancy to go and be like that."
United face Bayern Munich in the Champions League quarter-final second leg on Wednesday night.