The Toffees conceded an injury-time equaliser after coming from behind to earn a deserved 2-1 advantage courtesy of a Marouane Fellaini brace.
Having also had the majority of the possession and chances to extend their lead, Moyes has confessed that Steve Sidwell's late leveller was a difficult blow to take.
He said: "It feels like a defeat. We conceded a shocking goal to allow them to equalise at the end. We're as sick as it gets."
Despite dropping two points late on, the draw was enough to see Everton climb back into the Premier League top four.