Substitute Trundle converted after excellent work from Nathan Dyer but saw his effort disallowed for handball.
The Swans went into the game needing a win and Blackpool to drop points to earn a place in the season’s finale.
But despite the Seasiders only managing a 1-1 draw against Bristol City, it was the same old story for the division’s lowest scorers as the Swans were made to pay for a lack of composure in front of goal.
Swansea started the brighter of the two sides and nearly created an early opening but Leon Britton could not find Shefki Kuqi after a clever run.
And the hosts should have given their partisan support something to cheer about in the seventh minute but Kuqi blazed over after beating the offside trap.
Paolo Sousa’s side continued to press forward but struggled to overcome Doncaster’s solid backline.
The noise levels inside the Liberty Stadium went up a few decibels when news of Bristol City’s opener at Blackpool filtered through and the extra support nearly had the desired effect but Kuqi failed to convert David Cotterill’s excellent ball.
Despite failing to enjoy any real spells of possession, Doncaster looked dangerous on the counter attack as Ashley Williams did well to intercept James Coppinger’s dangerous cross.
City’s dominance continued, though, with Dyer looking especially threatening.
And they spurned another good opportunity midway through the half when Kuqi found Darren Pratley who failed to get any power behind his effort.
The home side continued to dominate but were again thwarted as Mark Gower’s fizzing low drive forced a smart save from Benjamin Smith before Pratley saw an effort deflect inches wide.
The Swans’ lack of composure in front of goal continued as Pratley somehow managed to miss from six yards just before half-time.
Sousa’s side continued where they left off at the start of the second half with Pratley spurning another great opportunity, pulling his shot wide.
The home support thought their side were ahead in the 49th minute but Cotterill’s effort hit the side netting.
As the tension around the ground increased, Doncaster started to come into the game with Coppinger forcing a save from Dorus De Vries.
Clearly rattled by the news of Blackpool’s equaliser, Sousa brought on Gorka Pintado for Gower in an attempt to get the opener.
The change failed to have the desired effect, though, as Sousa decided to again make changes, ignoring fans’ favourite Trundle, instead bringing on record-signing Craig Beattie.
And the former Celtic man should have made an instant impact when he was clean through but he failed to get the ball out of his feet, allowing James O’Connor to get back.
The City boss finally did bring Trundle on with 11 minutes to go but it was Cotterill who created the game’s next chance when he hit wide.
The hosts’ fate could have been sealed with a minute to go but Paul Heffernan spurned a great opportunity to give Doncaster the lead.
It did not matter, though, as the game finished 0-0 despite Beattie having a penalty appeal turned down and Trundle’s effort being chalked off.