Forest created enough chances to win by a comfortable margin, but Henri Lansbury, Andy Reid and Billy Sharp were all denied by the woodwork, while Reds goalkeeper Luke Steele produced a host of top-drawer saves.
The stalemate means that Forest missed the chance to return to the top six and they are two points adrift of sixth-placed Bolton with two games to go.
Barnsley will be more than happy to take a draw as they were barely able to get out of their own half, but it goes a long way to helping their fight against the drop as they are a point adrift of safety as the season enters its climax.
A run of five games without a win, with the last two being defeats, saw Forest come into this game needing a victory to reignite those top-six designs and they started on the front foot.
They could have been celebrating an early goal, but after good work by Elliott Ward and Radoslaw Majewski, Simon Cox's shot was deflected just wide.
Forest's domination continued and they came even closer to breaking the deadlock midway through the first period when Lansbury climbed highest from Majewski's corner, but his header hit the bar and Barnsley survived.
The Tykes, desperate for points for their own ambitions at the other end of the table, could not stem the tide and were reliant on goalkeeper Steele to keep them on level terms.
First he palmed away Sharp's header and was then equal to Adlene Guedioura's fierce effort from distance.
David Flitcroft's side were fortunate to get to the break with the scoreline at 0-0, but there was no respite for them after the restart.
Martin Cranie cleared off the line after Steele was unable to collect, but the stopper was back to form moments later when he superbly kept out Lansbury's diving header.
Forest's pursuit of an opener was incessant, with Steele at it again as he superbly tipped Reid's effort onto the post before the woodwork was rattled for a third time of the afternoon when Sharp hit a volley into the upright.
Danny Collins headed over as Billy Davies men continued to push for a winner, but Barnsley somehow held on, with Forest now up against it in the play-off race.