Chelsea's victory was their first in three games, building on their spirited fightback from two goals down to draw 2-2 against Liverpool on Sunday.
"It seems like a deserved win, an excellent result because it reflects the game. We could have scored more but it is hard to score against Tottenham," Tuchel said.
"We did create a lot, some huge chances. The up-side is everybody knows it is going to be a tough match in the second leg. It's not decided yet."
With Romelu Lukaku back in the fold, albeit once again looking far from his best, Tuchel will hope he has navigated a storm that threatened to derail Chelsea's season.
Lukaku, Chelsea's club record £97.5 million ($132 million) signing from Inter Milan last year, was dropped for the Liverpool game after he gave an interview that featured criticism of the way he was being used by Tuchel.
But Tuchel said he held "calm" talks with the Belgium striker on Monday and restored him to the team to face Tottenham after he issued an apology.
"I was pretty sure he was not affected. Even the last days he seemed relaxed, fine with the situation and mentally moved on," Tuchel said.
"Romelu can handle pressure and adversity, it was a good performance, he contributed a lot to our defensive set up and had chances."
'It was a difficult game'
Ironically, Lukaku's return came against Tottenham boss Antonio Conte, who got the best out of him during their Serie A-winning spell together at Inter.
Conte was back at Chelsea for the first time since being sacked in 2018 despite winning the Premier League and FA Cup in his two-year reign.
The Italian claimed earlier this season that Chelsea had yet to work out how to get the best out of Lukaku, but he has plenty of work to do with his own team on the evidence of Tottenham's spluttering display.
"It was a difficult game. Chelsea were much better than us. If you compare the teams there is not a comparison," Conte said.
"Today we have seen the difference between the teams. If we think we are close (to Chelsea), I think we are not in the right way."
Lukaku was greeted with surprisingly little venom from the Chelsea fans, a reception perhaps helped by their side making the perfect start in the fifth minute.
Japhet Tanganga played Emerson Royal into trouble deep inside the Tottenham half and Marcos Alonso pounced to steal possession.
Alonso slipped his pass behind the out of position Tanganga to Havertz, whose close-range shot deflected in off Davinson Sanchez for his first goal since 6 November.
Although Chelsea were without Thiago Silva and N'Golo Kante after they tested positive for the coronavirus, the European champions dominated from start to finish.
Lukaku had a role in Chelsea's second goal in the 34th minute as his persistence drew a foul from Sanchez.
Hakim Ziyech's free-kick should have been easily dealt with by Tanganga, but the hapless centre-back headed it straight at Davies, who had no chance of getting out of the way as it rebounded off his shoulder into the net.