Reds manager Jurgen Klopp was hoping his side could clinch their second piece of silverware in a little over two months, however, it wasn't to be on the day.
Liverpool found themselves behind in the opening fifteen minutes as Raheem Sterling converted from close-range to put City 1-0 up.
The Reds, who looked lacklustre in the first-half, improved their performance after the break and created several chances - hitting the woodwork on two occasions.
Despite Salah, Naby Keita and Xherdan Shaqiri all coming close to giving the Reds a comeback victory, the two sides were level after 90 minutes.
It was City who emerged 5-4 winners after the penalty shoot-out as Gini Wijnaldum saw his penalty saved by Claudio Bravo - before Gabriel Jesus stroked in the winner.
Slide through our gallery below for the best snaps from a disappointing afternoon for the Reds.