Ten Hag went into the final rocked by reports that he would be dismissed regardless of the result at Wembley.
But United's beleaguered manager made a convincing case to remain in charge as he out-witted City boss Pep Guardiola to deliver the second trophy of his turbulent two-year reign.
Now Ten Hag must wait to discover his fate after insisting he had not been told if he will be axed.
United co-owner Jim Ratcliffe and members of the Glazer family, who are the club's majority shareholders, celebrated the team's first FA Cup triumph in eight years from the Royal box.
It remains to be seen whether that will be enough to save Ten Hag after United finished eighth in the Premier League -- their lowest final position since 1990 -- and crashed out of the Champions League at the group stage.
United were beaten 14 times in the league -- including humiliating losses to Crystal Palace and Bournemouth -- finished with a negative goal difference and came 31 points behind champions City.
Yet Ten Hag is adamant United are heading in the right direction under his guidance.
And in a defiant post-match press conference, the former Ajax boss made it clear he did not fear the sack.
"When I started here, I said I'm here to win, also I want to build a team. Both I'm doing," he said.
"If they don't want me, I go anywhere else and do what I did my whole career, winning games and trophies."
Asked if he had received any assurances that his job was secure since the reports of his potential dismissal, Ten Hag said: "That is what they always tell me (in the past).
"Every time it is the same question. They don't have to tell me every week.
"I don't think about this. I'm in a project and we are exactly where we want to be. We are constructing a team for the future."
'It was a mess'
United have been linked with former Chelsea boss Mauricio Pochettino, ex-Bayern Munich coach Thomas Tuchel, England manager Gareth Southgate and Ipswich chief Kieran McKenna.
Pressed on whether reports that United had talked to prospective replacements for him was disrespectful, Ten Hag said: "I don't know if they have done this. I can't answer this.
"I don't have to make this decision. In the last decade there were not so many trophies and finals for this club."
Beating a City team that clinched an unprecedented fourth successive Premier League last weekend was undoubtedly a feather in Ten Hag's cap.
The Dutchman, who ended United's six-year trophy drought by winning the League Cup last season, could take credit for an astute game-plan and he admitted it was a sweet success in the circumstances.
"If you play at this level against the best team in the world, then I'm very happy," he said.
"The FA Cup was absolutely one on my bucket list. It is a huge trophy. I'm so happy we won because it was a team performance.
"When I took over it was a mess at United. We will go with ups and downs but the team plays with an identity.
"We are exactly where we should be. We have values in the squad, the team is progressing. Two trophies in three years is not bad. Three finals as well, but I'm not satisfied."
Ten Hag appears to have the support of his players, with Lisandro Martinez lifting him into the air in celebration when the final whistle sounded, before he was embraced by many of his players.
Ten Hag was cheered to the rafters by United fans when he held up the Cup in the Royal box, kissing it and repeatedly shouting "yes" as he gestured towards the celebrating mass of red in the Wembley sunshine.
If Ten Hag has earned a reprieve, he made it clear more investment in the squad is needed to compete with City in the long term.
"When you don't have the players available, then you can't perform," he said of United's injury-plagued season.
"The depth in the squad is absolutely not good enough. We strengthened the squad with our coaching but we need transfer windows to bring in players who are always available."
