“So hopefully he’ll come in and have a little chat with me and I’ll try to pick his brain for five or 10 minutes. He’s absolutely at the top of his game, with world-class managerial qualities. Any young coaches like myself of course naturally try and emulate coaches like that.”

It was not reported if Mourinho did indeed uncork the bottle with the 36-year-old Johnson after the match, but the United boss said he was delighted for Championship side despite suffering defeat at Ashton Gate.

“I think a beautiful day for football,” Mourinho said. “Because a team from a lower division won and got into the semi-final. A big day for them and a big day for their supporters, so I congratulate them.”

The United manager isn’t usually so magnanimous, but then there is much to admire about Bristol City this season.

Eliminating the holders, through a goal in the third minute of stoppage time, was no fluke for the 123-year-old team without a major trophy to their name. United are the southwest England team’s fourth Premier League scalp after knocking out Watford, Stoke and Crystal Palace. City are also pushing to gain promotion to the Premier League for the first time.

But the reward for eliminating United is an even tougher semi-final over two legs – against runaway Premier League leader Manchester City in January for a place in the final against Chelsea or Arsenal.

“These players now will have a bond forever,” City manager Lee Johnson said. “A night like tonight will just cement that bond.”

The quarter-final was heading to extra time until a goal Johnson expects to “live in the memory for many generations” at the club. Korey Smith brought down Matty Taylor’s chipped pass on his chest and unleashed the ball on the turn under United goalkeeper Sergio Romero.

“A few times I’d made runs in behind and I wasn’t being tracked,” Smith said. “So I said at half-time to the boys, ‘If I make that run look for me and I’ll try and get that shot off.’ Luckily Tayls (Taylor) made a great ball and it’s gone in.”

City, who are renowned for elaborate pre-recorded goal celebration GIFs, quickly tweeted out a clip (above) of Smith wearing a Santa hat setting off a streamer that garnered more than 70,000 retweets or likes within two hours.

Celebrations in the stadium were more spontaneous, with thousands of fans flooding onto the field after a game that had seen Joe Bryan’s opener for City cancelled out by Zlatan Ibrahimovic on the striker’s first start of the season.

“In the first half, we lacked intensity that they had, and when I say intensity I say not just physical, I say also mentally,” Mourinho said after surrendering the first piece of last season’s treble. “For them, it is a big night, and in this club we know how to win and how to lose.”

Revenge was 108 years in the making for Bristol City, who lost to United in their only major final in the 1909 FA Cup. By next season, they could be in the same division. City are sitting third in the League Championship as they try to end a 38-year exile from the top flight.

“I joined the club when we were in League One [in 2014],” Smith said. “We had three stands and obviously we had a great season. And the next year we were in and around the bottom of the [Championship] table.

“This year we’ve been absolutely brilliant. The younger players are developing and people are coming into their prime. The stadium now is absolutely amazing. It’s nice to give the fans a season they’re enjoying so far.”

The other two-legged semi-final in January is a London derby between Arsenal and Chelsea, who beat Bournemouth 2-1 in Wednesday’s other quarter-final.

Willian tapped in Chelsea’s opener in the 13th minute, and extra time was looming after Dan Gosling curled in a 90th-minute leveller.

But Eden Hazard’s back-heel pass set up Alvaro Morata for the winner at Stamford Bridge. The striker was booked for excessively celebrating and will be suspended for Saturday’s game against Everton owing to an accumulation of yellow cards.