Indeed, Carragher feels the Merseyside outfit did well considering their gulf in quality compared to Manchester City - and their centre-back issues.
Liverpool went 1-0 down to City thanks to a Fernandinho goal but equalised late on after an extended period of pressure, Philippe Coutinho scoring the goal.
The Capital One Cup final went to extra-time and penalties but Man City were ultimately victorious at Wembley Stadium.
Liverpool certainly did do well against Manchester City, at times looking irresistible.
Most of the Reds also showed so much heart as they fought back from a goal down.
Ultimately, little of that will soothe the pain players, manager and fans feel. The same for Carragher, who remains gutted despite highlighting a positive for Liverpool.
The Anfield outfit can hope for more finals under Jurgen Klopp - but, naturally, less heartbreak.
Despite the disappointment, Carragher did joke about having a laugh with Manchester City fan Noel Gallagher after the game.