Rudi Garcia's men were not good enough in attack and stumbled in their attempts at closing the gap on Juventus at the summit of Serie A
The performance for the second-placed hosts was tepid at best and the first 45 minutes had only half-chances thanks to lethargic passing and an inability to break down Parma's defence.
The latter half was at least a little more representative of a team who are supposed to be challenging for the Scudetto, but Roma still failed to register a goal.
Ashley Cole arguably had the two best chances with the clock ticking towards the 90-minute mark, but his header struck the woodwork and a later effort was skied over the bar.
Rudi Garcia's men could have closed the gap at the top of Serie A to five points ahead of Juventus' clash with Cesena, but now they could fall 10 points behind the reigning champions by the end of the weekend.
Parma, meanwhile, ended a losing streak of five successive matches and secured only their third clean sheet of the entire season, but their future remains up in the air amid calls for spiralling debts to be paid by Monday.
Roma, who had Seydou Doumbia making his first start since signing for the club in January and Gervinho returning from Africa Cup of Nation final glory, were tentative in their early efforts and struggled to form incisive attacks.
A few minutes later, on the 25-minute mark, Ljajic tried his luck from 22 yards out but skewed over. The lack of accuracy and sensibility summed up the half for the hosts.
Ljajic was bustling for much of the match and, on the brink of the break, almost put the Giallorossi ahead after nutmegging Cassani en route inside Parma's box, but he angled his shot into the side-netting.
The second half dragged on tediously just like the first, with the home crowd becoming audibly more agitated with every misplaced pass and wayward half-attempt at a cross.
Gervinho and Radja Nainggolan both saw decent shots saved and deflected marginally wide respectively.
Garcia's men finally remembered they are battling for the Scudetto at the top of Serie A and kicked into gear with 25 minutes to play.
Nainggolan steered a volleyed effort just wide following a corner melee, then crossed superbly two minutes later, though Doumbia was unable to reach the back-post ball.
Roma were looking increasingly likely to be held to a draw, although left-back Cole had two gilt-edged chances in the final moments of the match to score a late winner.
Cole's first effort cannoned off his head and on to the post with seven minutes to go then, in the final minute of the match, the ex-England international thundered a close-range volley over the crossbar.