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The world number one showed his annoyance with a section of the 5,000-strong British support by cupping his ear and blowing ironic kisses at the end of the first set of his 6-4 6-4 victory over Cameron Norrie.

When the same group of fans began drumming during Djokovic’s on-court interview, the Serbian responded: “Learn how to respect players, learn how to behave yourself,” before adding, “no, you shut up, you be quiet”.

It was a sour end to what was a disappointing evening for Britain, with the writing on the wall once Jack Draper fell to a 7-6 (2) 7-6 (6) defeat by Miomir Kecmanovic in a opening rubber that was a must-win.

On his spat with the supporters, Djokovic said: “In the Davis Cup, it’s normal that sometimes fans step over the line but, in the heat of the moment, you react too, and you show that you don’t allow this kind of behaviour.

“They can do whatever they want, but I’m going to respond to that. I was trying to talk and they were purposely starting to play the drums so that I don’t talk and they were trying to annoy me the entire match. So we had a little bit of a chat in the end.”

Britain captain Leon Smith refused to criticise his side’s backers, saying: “That’s one of the things that’s good about Davis Cup and the team competition that actually you’re kind of meant to make noise.

“Whether there is a bit that goes over, comments, I could hear a couple – I don’t think it’s that bad. I would hate to see it quietening down, because there’s enough quiet tennis as it is.”

Britain’s dramatic success against France in Manchester in September had sent them through to the final eight event for the first time in the revamped format.

The tie did not get under way until 6.10pm, more than two hours later than billed, because of the over-running first match of the day between Italy and the Netherlands.

The near-capacity crowd, which also included a sizeable number of Serbian supporters, gave the event the sort of authentic Davis Cup feel that has so often been missing since the switch from the home-and-away format.

Among those sat in the stands at the Palacio de Deportes Martin Carpena was Dan Evans, who had hoped to build on his brilliant performances in Manchester before a calf injury prematurely ended his season.

But even the British number two would have had his work cut out against an inspired Kecmanovic, who was chosen ahead of the higher-ranked Laslo Djere and fully justified the decision.

Draper had the better form coming in having reached his first ATP Tour final this month and had beaten Kecmanovic – ranked five places higher at 55 – earlier this year, but the Serbian was dominant on serve and edged two tie-breaks.

It was only 21-year-old Draper’s second Davis Cup rubber and he admitted knowing Djokovic was looming added to the nerves he felt.

“That’s seemingly a must-win match for me,” said Draper. “It’s definitely a tough challenge to go out there knowing that there is a lot more pressure on me to win the match.

“That’s the kind of pressure that, if I want to be a top player, I have to cope with and have to perform under. It’s tough not to get the win today. I gave it all I had mentally. I didn’t do a few things as well as I wanted to, but he played a great match.”

Djokovic had lost only six of his 61 previous matches this season, with just one defeat since the Wimbledon final, while his Davis Cup record is utterly formidable.

It is 12 years since he lost a singles match in the competition, and even that was by retirement, with now 21 straight wins and only four sets dropped.

Norrie had managed only a single set in three previous meetings and has endured a miserable run since the clay-court swing back in the spring, but he was captain Leon Smith’s only option once Andy Murray pulled out with a minor shoulder injury.

He did not put in a bad performance by any means, but was fire-fighting from the moment he was broken at 2-2 in the opening set and won only eight points on Djokovic’s serve during the contest.

“I was just trying to go in and challenge him,” said Norrie. “I was kind of proud of how I competed, but it was still tough to lose that one. But I could see him hurting a little bit down at the other end, so that was good and a good test for my game.”

While Serbia are a step closer to the trophy, Britain must start again in February in the qualifiers – barring an unlikely wild card through to September’s group stage.

Smith added: “It’s disappointing. It feels like a lot of prep for one day of matches. We’ve lost in the quarter-finals here, but we’ve won four, lost one this year. It’s a good record. It’s a good year.”