Havertz’s fifth goal of the season put Chelsea in charge against a miserable Spurs but the Germany forward suffered a nasty broken finger in the tumble that followed his early finish.
The 22-year-old battled on until half-time when he was forced to give up the ghost amid mounting pain, but Chelsea still produced a fine result amid a makeshift set-up and against a strong Spurs XI.
Chelsea made a last-minute switch to a back four after Thiago Silva and N’Golo Kante tested positive for Covid-19 on Wednesday morning.
And Tuchel paid tribute to Chelsea’s players for shaking off the mounting injury and coronavirus-enforced absentees to put one foot in the League Cup final.
“Kai has the issue with his finger, he broke his finger and it looked horrible,” said Tuchel.
“And he played through the pain that was getting bigger and bigger. He survived until half-time and then we had to make the change.
“I liked our performance a lot. We looked full of confidence and had two late last-minute pieces of bad news with Thiago Silva and N’Golo Kante, who were both supposed to start.
“So we decided at the last minute to maybe switch to a back four. The guys were very committed and very open to that, to making such a late change.
“And it was a very strong performance, so it was a well-deserved win in a big match against a very strong opponent.”
Centre-back Silva’s positive Covid test further depletes Chelsea’s defence, with Andreas Christensen out with a back problem and Ben Chilwell and Reece James long-term absentees.
Captain Cesar Azpilicueta went down late on and hobbled out of the clash in the closing stages, but appears to have avoided a serious issue.
Tuchel added: “We were very worried but Azpi says it’s only a cramp and not an injury. So that would be good news and we trust him.”
Ben Davies put through his own net for a bungling own goal as Spurs struggled in boss Antonio Conte’s first return to former club Chelsea.
Chelsea squandered a hatful of chances to settle the two-legged affair midway through the tie, leaving the Blues’ German boss urging caution ahead of next Wednesday’s return encounter.
“We could have created a bigger cushion, yes, it was possible; we created a lot,” said Tuchel.
“But we were very, very strong, and it’s so hard to create chances against Tottenham. But especially in the second half we created a lot of big chances for a third or fourth goal.
“So everybody knows it’s not fully decided, and we need another 90 minutes of top-quality football if we want to go through.”
Romelu Lukaku was back up front for Chelsea after his weekend omission owing to internal disciplinary wrangles.
I’m happy with his performance, I like how he played, strong, huge commitment in defensive work
The club-record £98million recruit had fallen into hot water with the Blues after revealing unhappiness at Stamford Bridge in a recent interview.
Lukaku missed Sunday’s 2-2 Premier League draw with Liverpool, but has since apologised to all at Chelsea and the club’s supporters, and accepted a fine.
The former Inter Milan star nodded wide from a glorious Hakim Ziyech cross, but Tuchel was still impressed by the 28-year-old’s night.
“I’m happy with his performance, I like how he played, strong, huge commitment in defensive work,” said Tuchel.
“He was always dangerous, always used his body, and was always involved in dangerous situations. I expected it honestly because Romelu can handle pressure, he can handle adversity, and he seemed to be relaxed after the decision was made and we finished our talks. I felt him relaxed enough to have a performance like this.”
A deflated Spurs boss Conte insisted Tottenham can only be rated as a mid-table Premier League team, urging patience and time on a major rebuilding job to catch up with England’s top teams.
“We need to have patience because there is a lot, a lot of a job to do, in many aspects,” said Conte.
“Because in the last few years the level of Tottenham has dropped, and dropped a lot. And now we have to rebuild, and we need to have patience and more time.
“We are working a lot, to try to fight in this league, but in this moment we are in the middle.
“That’s our situation, we are in the middle. Not up, not down, we are in the middle.”
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