United triumphed 2-1 against St Mirren at Fir Park after substitute Thomas Mikkelsen headed home a winner following Simon Murray's 74th-minute cross.
St Mirren had the better of the first half and they levelled through Rory Loy within 60 seconds of Tony Andreu's brilliant volley in the 37th minute.
But United restricted the Buddies to few chances after the break and they had several opportunities to score a third on the counter-attack.
The Tayside club have dropped to fourth in the Ladbrokes Championship in recent weeks after winning only once in 10 league games but victory at Fir Park provided some much-needed cheer as they fight for promotion.
"I'm extremely delighted for everybody," McKinnon said
"It's been a tough journey for the fans in the last year.
"Relegation has left its scars so hopefully that's part of repaying the fans for their patience and their loyalty.
"We are delighted to give them a trophy and I'm also delighted for the players because we have shot ourselves in the foot in recent games and that was another prime example
They scored their goal but we kept on, kept the message, keep passing the ball, and I thought they were excellent."
St Mirren manager Jack Ross feels his players should have few regrets other than not taking more first-half chances.
When asked for his thoughts, Ross said: "First and foremost to congratulate Dundee United
I said often enough pre-match that a cup final is about winning on the day
They have done that so they deserve plaudits for it.
"I thought we were good, I thought we were on the front foot for large parts, I thought we created the clearer opportunities through the game, so from that perspective I have absolutely no complaints over my team's performance.
"I thought they produced a performance worthy of a cup final
They haven't got the rewards on the day but we played against a good team who scored two really good goals.
"I couldn't ask any more from my group of players."
Source : PA