City wasted two wonderful chances to claim the three points through Edin Dzeko and David Silva, adding to their frustration after Jones turned away appeals when the Bosnian went over Chico Flores just inside the box.
Predictably, with in-form City having an FA Cup final to look forward to and Swansea already safe with the League Cup safely locked away, the first 20 minutes were typical end of season fare.
Aside from a couple of half chances for Samir Nasri there was little incident of note.
Eventually it was Swansea, celebrating the 10th anniversary of the win against Hull which saw them avoid relegation from the Football League, who were the first of the sides to rouse from their slumbers.
The first opportunity arrived in the 17th minute, Angel Rangel and Nathan Dyer combined to great effect down the right but Pablo Hernandez scooped the winger's pass feebly over the bar.
Nasri made a timely intervention to deny Routledge seconds later, before Michu's goalscoring touch again deserted him.
The Spaniard has struggled to maintain the superb form he showed over the first two-thirds of the season, and he somehow volleyed wide from six yards from Dyer's perfectly-weighted cross.
Hernandez, another player looking short of his best, became the latest to spurn a good chance just past the half-hour mark.Routledge played the former Valencia man in on goal, but he took too long to control before rolling a weak effort wide.
City, who started with Carlos Tevez on the bench, came close to punishing their hosts' profligacy when Gareth Barry's lovely pass floated over Ashley Williams to Nasri, but the Frenchman fluffed his attempted volley straight at Michel Vorm.
Referee Jones then made the first of his controversial penalty calls in the 38th minute.
Michu was clattered in the area by Nastasic having flicked the ball away from the defender, but Jones, to the bewilderment of those in white shirts, waved away the Swansea protests.
His refusal to award a spot-kick extended Swansea's run without a Premier League penalty, their last penalty came in this fixture in March 2012.
With Swansea perhaps dwelling on Jones' decision, City ended the half with their best passage of play, and only an examplary tackle from Williams and follow-up save from Vorm denied Silva after Nasri had got the better of Flores.
Mancini withdrew Yaya Toure at the break for Dzeko and City began to take a hold on the game, with Silva becoming increasingly influential as he attempted to pry open the Swansea backline.
But Vorm was rarely troubled, although City felt the Dutchman should have had to face a penalty just after the hour.
Dzeko cut in to the area from the City left and went over Flores as the Spaniard left a trailing leg, Jones once again answered in the negative to the fury of Mancini and his bench.
Even then, City should have secured three points.
Dzeko put in his contender for miss of the season six minutes from time as he missed an open goal from four yards, before the excellent Silva blotted his copybook by blazing wide when a loose ball fell to him 12 yards out.
Source: Manchester City MAD