Town boss Jim Magilton admitted his side are lucky to be in the draw for the fourth round of the FA Cup after a lacklustre performance at Chester's Deva Stadium.
Magilton said: "We were second best today. Chester headed, scrapped and won all the second balls. Their front two were lively and they caused us all sorts of problems.
"They made it difficult for us and we didn't have enough people show any real desire to be brave and get on the ball. Chester will feel aggrieved that they have not won today.
"It was a tough day for us, but the only saving grace is that we are still in the hat and I am very relieved about that. We know that we will have to be better next time but hopefully home advantage will swing it our way.
"A replay is the least Chester deserved. They were better than us in many areas and I was really disappointed with our performance.
"It was chalk and cheese compared to our performance against Birmingham last week. We didn't do the 'nasty' side of the game well and didn't show enough desire to win a football match.
"The players have got to learn you don't just turn up and win games. We seemed to have people out there who thought it would be a case of just putting the shirt on.
"It's another step we have to overcome because we need to be turning in good performances week after week, regardless of the opposition. To do that you have to earn the right to play.”
Chester boss Mark Wright was pleased with his side's display: "I'm very proud of the boys. Ipswich have got some really exceptional players and we were probably hanging on at the end, but I thought on the whole we more than dominated them.
"We started ever so well and each and every one of my players gave everything they had and maybe on another day it could have gone our way. I think with the chances we had we should have won, but it wasn't really down to luck, but poor finishing. The only thing we were missing was a couple of goals.
"Today they gave us 90 minutes and I can't say any player let me down. The cup is a great leveller and, even though there are 49 places between the sides, I don't think that matters in the cup because on their day any side can beat anybody."