This result leaves the Swans languishing in the lower reaches of the Championship after they largely dominated but failed to break down a resolute rearguard display from Gary Johnson's men.
Sousa recalled fit-again midfielder Joe Allen after a hamstring injury which had sidelined him since the opening day of the season and he replaced Leon Britton in the starting line-up.
New recruit Cedric van der Gun made his full debut, replacing Mark Gower on the left flank, while Gorka Pintado came in for the ineligible Lee Trundle.
The visitors were forced into five changes as Nicky Maynard (stomach bug), Dean Gerken (illness) and Louis Carey (knee) were all left sidelined through injury.
Brian Wilson and Cole Skuse dropped to the bench while goalkeeper Adriano Basso returned for his first start of the season.
Bradley Orr, Lee Johnson, Ivan Sproule and Evander Sno were also handed starting berths while Christian Ribeiro missed out with a knee injury picked up on Wales duty.
Swansea threatened first in the sixth minute when Allen collected possession and hit a fierce 20-yard shot over the bar.
Yet the visitors went desperately close in the 11th minute when an inswinging corner from Jamie McAllister was greeted by a firm header from Liam Fontaine.
Swansea goalkeeper Dorus De Vries, who excelled during Saturday's 2-0 defeat at Preston, superbly tipped the ball around the post.
Sproule then tried his luck 20 yards but Swansea defender Ashley Richards made a fine block to avert the danger.
Richards then showcased his quality at the other end of the field with a right-foot shot from six yards which flashed just wide of the far post.
The visitors should have led in the 22nd minute when Orr crossed from the flank and Marvin Elliott headed just over the bar from 12 yards.
Sno then drilled a shot wide when well placed as the Robins enjoyed a brief spell of sustained pressure which could have seen them forge ahead.
Yet the pendulum swung back towards Swansea in the 33rd minute when Nathan Dyer narrowly failed to hit the target from close range.
Pintado warmed Basso's hands from distance shortly before the break but the deadlock was almost broken midway through the second period when defender Ashley Williams headed over from 12 yards.
Swansea substitute Craig Beattie looked lively when he entered the action and in the 74th minute he went close with a predatory left-foot strike which drew another smart stop from Basso.
As the game entered the final stages a flurry of chances came and were spurned by both sides.
Substitute Ferrie Bodde fired right-footed from 35 yards before Lee Johnson shot straight at Basso in the 77th minute as neither side could find a way through.
Basso excelled again in the 89th minute when he tipped a 12-yard shot from Jordi Lopez around a post.