Nathan Dyer was unfortunate to see his early strike come back off the post and Shefki Kuqi headed wide right at the death, but Ipswich deserved a point which moves them nine points above third-bottom Crystal Palace.
Swansea have now drawn nine home games this season and they will be hoping those dropped points will not prove costly at the end of the season, while the draw for Ipswich was their 18th of the season which equals the club record.
Sousa urged his players to focus after their midweek thrashing at Blackpool and Dyer almost gave them a dream start but his right-foot drive from close range struck the post after just two minutes.
But that proved to something of a wake-up call for Keane's side, who rolled up their sleeves and started to frustrate the home side.
Not for the first time this season the Welsh side enjoyed plenty of possession but were finding it difficult to break their rivals down.
Ipswich were also finding goalscoring opportunities hard to come by with David Norris trying his luck from long range but failing to test Dorus De Vries in the Swansea goal.
De Vries was called into action seven minutes before the break but made a comfortable save from Grant Leadbitter's long-range strike.
Daryl Murphy had a chance to put Ipswich in front just after half-time but the on-loan Sunderland forward failed to beat Dutchman De Vries from an acute angle.
The Swansea fans were irate when the linesman failed to raise his flag as Walters, who appeared to be clearly offside, raced into the box and cut the ball back for Murphy and his shot was tipped around the post by the alert De Vries.
Swansea fashioned a rare chance on the hour-mark but former Ipswich striker Kuqi was unable to hit the target with a header from 12 yards out.
Sousa brought on Joe Allen for the ineffective Andrea Orlandi with 25 minutes remaining as the home side looked to exert some pressure on the Ipswich defence.
Kuqi could have won it late on but the Finland striker was unable to test Brian Murphy with a poor header which summed up an uninspiring game in South Wales.