Everton jumped to a 2-0 lead at Goodison Park through Beto and Dwight McNeil before halftime, though Ipswich were able to fight back to earn the point thanks to goals from Julio Enciso and George Hirst.
“We're disappointed,” Moyes admitted. “We never shook Ipswich off, really. They were always there or thereabouts. We just couldn't quite get enough.
“I thought we did a lot of good things. We've tried some different things today as well to see how players play in different roles.
“I thought we did really well in the opening part of the game for 30 minutes or so. I thought we played really well and got the goals eventually.
“But I think the goal just before half-time for them just sort of rocked us a little bit. It always gave Ipswich something to go at and we couldn't quite get the third goal to get ourselves clear.”
Ipswich a tricky team
Moyes admits they struggled to contain Ipswich at times on the day.
He added: “I thought there were a lot of good things about us – we controlled a lot of the game – but they are a tricky team, Ipswich, which people will know if they've watched a lot of football. They build up very well from the goalkeeper, out through the team and up to the front line.
“So we had that to cope with in the first half but I thought the two goals we scored to get ourselves in front were thoroughly deserved.
“Then we gave up a goal, which was pretty slack from our point of view but, obviously, it was a wonderful finish from the boy (Enciso), so we'll hold our hand up to that.
“I thought the second half we had a lot of the ball and dominated it. We got some really good crosses and balls into the box but there were a lack of shots on goal."
"Did we deserve the point?"
Indeed, Moyes admits Ipswich finished the better team as momentum was with the visitors.
He said, "I don't know if we truly deserved to draw the game, but then we might not have done enough to get it over the line to win in the second half.
“I thought we made a couple of terrible decisions, a couple of players on the pitch for the second goal regarding runs and tackles and whatnot when neither were needed and we sort of left ourselves a bit exposed.”