Jose Mourinho conceded Manchester United had been fortunate to beat Southampton in the EFL Cup final but that he was relieved to have won his first trophy at the club.
The United manager also again praised the contribution of their matchwinner Zlatan Ibrahimovic, before insisting he had no plans to "beg" the striker to sign a new contract.
Their 3-2 victory at Wembley Stadium not only brought Mourinho level on four League Cup victories with Sir Alex Ferguson and Brian Clough, but it made him the club's first ever manager to win a major trophy in his first season there.
Success looked in doubt throughout much of a second half dominated by Southampton after Manolo Gabbiadini's second goal had made the score 2-2 after Ibrahimovic's free-kick and Jesse Lingard's finish had given United the lead.
Against the run of play Ibrahimovic's second, in the 87th minute, restored their advantage, before also ensuring a continuation of Mourinho's fine record in English football.
"First of all, the man that just left table (Southampton manager Claude Puel) has a reason to be really sad and disappointed," said the Portuguese, 54.
"His team did fantastic work, deserved extra time, and to lose in the 87th minute gives very little time to try to react.
"It's a bit unfair for them. They gave us a beautiful final, a beautiful match.
"I'm obviously very happy with the victory, with the fact that I did it four times, the same as Mr Clough, and with a chance to win for a fifth time.
"The game was broken at 2-2. We were lucky to be 2-0 (up). Then 2-1 changed completely the direction of the game. Obviously the 2-2: a phenomenal goal. Technically it's such a difficult shot. Then the game is broken."
Despite looking glum, Mourinho reiterated: "I am very happy. I always try to put myself in the secondary position - it's important for the fans, the club, the players - but it's also important for me.
"I put a lot of pressure on myself; you put a lot of pressure on myself. I wanted very much to win a major trophy at every club; by doing that with Manchester United it's quite the sense of relief because it was a big target for me.
"The reality is that we want more: my contract is long, I have two more years with this one, so hopefully I can win more. This season I know it's difficult, but the reality is we have to try to fight for more."
Mourinho was then asked why he had had such faith in Ibrahimovic, then aged 34 and considered in decline, when he recruited him last summer.
He has made the striker so central to United's plans that he has also marginalised club captain Wayne Rooney, and in a country in which he was previously thought to not be a big-game player.
"I was his manager, I know his potential," he responded. "Only a silly player comes to England at 35 years old, and with the successful career that Zlatan has, if he doesn't feel he can do it.
"Who better to know? Him. Not me, not you. Him. To take the challenge to come to a country like England, to a club like Manchester United. It's his credit, not my credit. I don't take him here if he doesn't want to come, if he's not ready."
Ibrahimovic's future remains the subject of speculation given his contract expires at the season's end, and Mourinho said: "I never beg for a player to sign a contract. I never beg for a player to play for me.
"One day Zlatan decided to (leave me and Inter Milan to join) Barcelona, I was very sad, but I did nothing to try to stop him to go, so I don't beg for players.
"But, if needed, maybe United fans can go to the door of his house, and stay there all night, if needed. We all want, and believe, that he is going to stay another season.
"It's one of these finals that I don't like. I like the finals like before, Chelsea-Manchester United, Chelsea-Arsenal, Chelsea-Liverpool, Chelsea-Tottenham.
"These are the finals I like, because you are not the favourite; you don't have more responsibility on your shoulder. This game is tricky, it's a tricky final."
Southampton had been unfortunate when, at 0-0, Gabbiadini had an early finish wrongly disallowed for offside.
Their attacking threat meant they also deserved to take the lead at 2-2, and their manager Claude Puel became the latest to call for the introduction of video technology.
"I would like of course the video for the future, for this situation for example," said the Frenchman, 55.
"For the moment in football without video, and just sometimes a bad decision and against us for the team.
"It's important to accept this but I am disappointed for the players and for the fans.
"It's very hard when we see this game to lose this game but it's football.
"Before the third goal we had the best situation, the best opportunities (to win).
"It is a big disappointment with the quality of this game. (And a) f rustration of course for all my players."