Boss Jim Magilton admitted that Town's 3-0 victory over Chesterfield was "scruffyâ€Â, but hoped that the win would help instil confidence in his players. Goals from Jon Walters, Pablo Couñago and Jon Stead won the first ever clash between the sides.
Magilton said: "I'm a firm believer that cup runs and league form can run in tandem. If you can continue to win cup games, hopefully confidence will build.
"It was a scruffy, scrappy win at times. I thought for 30 minutes they were excellent and put us on the back foot.
"We found it difficult at times. We just lacked a little bit of composure in the first half. We gave the ball away cheaply.
"I think the difference between the two sides was we were better in the final third.
"They had a chance right after we scored the penalty. Had they taken it, it might have been a different story.
"I think Chesterfield deserve an awful lot of credit. They came and had a go."
Magilton felt there was little doubt regarding the spotkick: "It looked a clear-cut penalty. It was unfortunate for the lad, but the referee was on top of it and Jon put the ball away well from the spot.
"Pablo and Jon Stead took their goals well and we need to take the confidence we will get from the win into next Saturday's game against Sheffield Wednesday.
"Iván Campo showed his experience and his class with his composure on the ball and it was good to get another clean sheet.
"We are in the hat for the next round and that is the main thing.
"It was important for the players to get another win under their belts to build on last week's victory at Derby and, although it was a scrappy performance, we will take the place in the next round."
Spireites boss Lee Richardson was less than impressed with substitute referee Gary Sutton's decision to give the Blues a spotkick, original official Keith Hill having limped off early on with an injury.
Richardson cited the change as an important factor in his side's defeat: "I thought there were two key moments in the game - the first half replacement of the referee and the decision to give a soft penalty.
"I think if you see the penalty again you will see there was no intent. It was a harsh decision. I don't think the margin of victory was merited.
"If we had gone another 10 minutes at 0-0, the crowd gets edgier, the Ipswich players get edgier. We might have been able to get a few chances ourselves."