The Red Devils have the best record on the road in the Premier League and cruised to a 4-0 win at Newcastle on Saturday to keep their European hopes alive
Although the Red Devils sit sixth in the Premier League, having struggled in their first season under their Scottish coach, the club have picked up more points away from home than any other club in the top flight.
A 4-0 victory at Newcastle United on Saturday represented the 10th league triumph on the road for the defending champions this season, yet Moyes has overseen just seven wins from 16 league games on home soil.
"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 former Everton boss 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, who face Bayern Munich on Wednesday in the second leg of their Champions League quarter-final, were hampered by injuries at St James' Park, having lost Wayne Rooney to a toe problem prior to the match.
Ashley Young was forced off in the first half after hurting his hand, while Patrice Evra and Marouane Fellaini were withdrawn after the interval.
"Pat Evra had a bit of a sore knee, Ashley Young looks like he's torn the ligaments in his hand and Marouane Fellaini was dizzy," Moyes added.