Moyes, who succeeded Sir Alex Ferguson in the summer, told Sky Sports News: "There will be [light at the end of the tunnel] because it is a transitional period and that was always going to be the case.
"I hoped it wouldn't have been as poor as it has been in the last few games. When I came here I knew it was never going to be easy and it's proved to be that way. I think the United supporters have been great to me and great to the club.
"They understand there is a big transition going on here and, like me, I don't think they expected us to have lost five games at this stage of the season. We didn't expect that, but I think they understand that there is a change going on. We'll work, try to improve and try to get better."
The result leaves United ninth in the Premier League.