Michu for Swansea and substitute Edin Dzeko for Man City both missed glorious chances to score but with little to play for neither side had the cutting edge needed to find the breakthrough.
Swansea began the brighter of the two teams with the visitors looking lethargic in the early stages and it was the home side that carved out the first few openings.
Good work from Angel Rangel and Nathan Dyer allowed the latter to cut the ball back for Pablo Hernandez but the Spanish winger could only loft his shot over the bar when well placed.
Michu had an even better opportunity to open the scoring after 20 minutes but skewed his sidefoot volley wide of the far post after another measured cross from the right by Dyer.
The high-profile visitors had barely got started at that point but they did manage to force Michael Vorm into action 10 minutes before the interval when Samir Nasri volleyed straight at the keeper.
Vorm produced another smart save just before the break as he smothered Sergio Aguero's effort from close range after Ashley Williams had done brilliantly to block from David Silva.
By that point, Swansea were cursing their luck after being denied a penalty for what seemed a clumsy challenge in the area by Matija Nastasic as he clattered into the unlucky Michu.
Roberto Mancini introduced Dzeko for Yaya Toure for the second half and, curiously, this appeared to help the visitors dominate the midfield through Gareth Barry and James Milner.
Dzeko could have been awarded a penalty just after the hour mark when he went down under a challenge from Chico Flores that would surely have resulted in a free-kick elsewhere on the pitch.
If Dzeko was feeling sorry for himself then he had nobody else to blame when he missed the target from close range inside the final 10 minutes after good work from Pablo Zabaleta.
Silva also had the opportunity to break the deadlock late on but placed his sidefooted effort wide and such wayward finishing meant the two teams were forced to settle for a point apiece.