But for the 13th time this season, the Tractor Boys were forced to settle for a single point rather than a full compliment when Steve Howard levelled for the Foxes eight minutes before the half-time whistle.
Lloyd Dyer was the creator, cutting in from the right before teeing up the veteran striker to poke the ball beyond Arran Lee-Barrett.
Keane, whose side lie 20th, said afterwards: "It was probably a fair result. We did have some good chances but our keeper pulled off the best save of the game. It was not a classic but to draw the game with an element of disappointment is a mark of our progress because Leicester are having a good season.
"I'm disappointed we didn't build on our great start to the game but I know we can do a lot better than today."
Keane admitted that his side needs to score more goals if they are to catapult themselves up the table.
He said: "What we lack at the moment is that we don't score enough goals and that's an area that needs improving.
"Draws won't get you too far up the table but I still think we are capable of having a good season, and that would include getting into the play-offs."
Keane revealed that new goalkeeper Brian Murphy could be sidelined for several weeks after he was injured in the pre-match warm up.
Former Swansea keeper Murphy, 26, signed for Ipswich in midweek after three years with Irish club Bohemians.
Keane said: "Murphy damaged ankle ligaments in the warm-up. He looked like he was in a lot of pain in the dressing room. He could be out for a number of weeks."
Nigel Pearson conceded his side had performed poorly.
The Foxes chief said: "It wasn't a very good game and we struggled to get anything going in a positive manner.
"We didn't achieve the standards we have reached this season.
"We didn't look as solid as we have been in recent games. We were too open and they - Ipswich - enjoyed some potentially dangerous situations.
"But at least we've come out of it with something positive."