Ryan Mason’s side struggled to assert control on proceedings throughout the 90 minutes at Wembley, and were second-best for much of the contest.
Aymeric Laporte scored the only goal of the game in the second half to give City their fourth successive League Cup title.
Spurs, meanwhile, lost their fourth consecutive final, having last won one in the same competition in 2008 under the stewardship of Juande Ramos.
Seven months later, Mason would make his professional debut for the club in a UEFA Cup tie against NEC.
Sunday was only Mason’s second game as a manager, having been appointed as interim manager until the end of the season following the departure of Jose Mourinho last week.
Carragher assesses Spurs cup final performance
Carragher said the club’s latest final defeat ‘had nothing to do’ with their interim manager, and criticised Tottenham players for their performances on the day.
He said on Monday Night Football: “This has nothing to do with Ryan Mason at all. This is a group of players who really lack courage, and basically bottled it in the final.
“Forget about losing the final, you don’t expect them to win against Manchester City, but it was how they went about it.
“A lot of people are talking about ‘if Jose was in charge’. Yes I thought it was a strange decision, but this is on the players.
“In this job I do a lot of people and other pundits say, ‘Typical Spurs. Spursy. They’re weak’.
“I fight against that because I think it’s lazy punditry. I’ve seen some brilliant Spurs teams.
“They’ve not won the league, not won the Champions League, but if I’m being totally honest I haven’t really expected them to.
“What I saw under Mauricio Pochettino for three or four years was outstanding, what I saw under Harry Redknapp for two or three years was outstanding as well.
“But the reason people speak about them in these terms is because of games like this.
“In their last four cup finals they haven’t scored a goal, and this performance is why they get stuck with this tag.
“I can’t argue for them, and Spurs fans can’t argue for them on the back of this performance. And it is on the players, nothing to do with the manager.”
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