City appeared set for a comfortable afternoon after goals from Sergio Aguero and Rodri put them 2-0 up inside half an hour.
Villa made a contest of the showpiece though, as Mbwana Samatta reduced the deficit before the break.
The soon-to-be deposed Premier League champions piled on the pressure after the restart but Villa managed to hold firm and nearly forced an equaliser late on to drag the final into extra time, but Bjorn Engels' effort was somehow kept out by City keeper Claudio Bravo.
Villa may have produced a valiant effort in the EFL Cup final, but it was a potentially damaging weekend for them in the Premier League as some of their key rivals picked up vital points.
On Friday night rock-bottom Norwich City claimed a 1-0 win over high-flying Leicester City and on Saturday West Ham saw off Southampton 3-2 as Bournemouth secured a handy point with a 2-2 draw with Chelsea.
In the late kick off on Saturday, Watford incredibly managed to end Liverpool's unbeaten run with a 3-0 win at Vicarage Road and Villa have now dropped into the bottom three.
It was almost a perfect storm of results going against Villa, with Brighton's home defeat to Crystal Palace the only positive, and immediately after the final loss Dean Smith admitted he had been keeping tabs on their relegation rivals.
Smith feels Villa can take plenty of positives from taking City so close on Sunday and he remains convinced his side can avoid an immediate return to the Championship.
"You can't not look at the results from yesterday and because we weren't playing we end up in the bottom three," said the Villa boss. "We have got a game in hand and if we take the performance from today into our league season then we will be OK."
Cup disappointments can have a huge impact on a team's league hopes and Watford are a prime example.
Last season, the Hornets reached the FA Cup final but lost out to Man City and the hangover from that defeat stretched deep into this season - as they lost their first three games and failed to pick up a win until November.
Such a run would be disastrous for Villa now with the games running out and Smith's task will be to rally his troops as quickly as possible ahead of next Monday's trip to Leicester.