The Irons blew a 3-0 lead to allow Arsenal leave London stadium with a point.
Moyes said, "We're nudging along and we're trying to hang in there with the top teams.
"We're trying to be competitive right until the end of the season and we know we're in a difficult run of fixtures.
"They're all difficult, but we'll have some fixtures near the end of the season which we might think we have a good chance in, and we had a really good chance today.
"You can't deny Arsenal just beat Tottenham and they just got through to the quarter-finals of the Europa League, so they're on a bit of a run at the moment and it was important to halt them so they couldn't get any closer to us, so hopefully we can keep well in front of them."
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