After months of speculation, Havertz finally joined Frank Lampard side for a reported £70m plus significant add-ons, making him the second most expensive player in the club's history after Kepa Arrizabalaga.
On Monday, he made his debut in a Chelsea shirt as the Blues defeated Brighton away from home, with the German being on the periphery of the action for the most part.
Even though such a fee will present certain expectations for Havertz, he says he won't be burdened by it.
"Of course, it's a big price tag, but I think in football today it is normal to pay these prices," Havertz said on Thursday.
"For me, I will not put a lot of pressure on myself because I think I have not done the worst thing in the past for the price tag to be that high, so I'm just trying to focus on my football, to try and play my best football at Chelsea and not to put that pressure on myself.
The 21-year-old did admit that he will take some time to adapt to his new surroundings, however.
"I think I've settled in very well," he continued.
"Of course, Chelsea is a very big club and for me it's a big step to come to another country, another culture, another language, it's very different than before and of course that needs some days, some weeks to adapt.
"It's a very big step to come from Leverkusen to the Premier League, it's another way here to play football. As a kid I watched the Premier League a lot, for me it was always the best league in the world, with the best teams, and I'm now very happy to play in one of the best teams in England and the world as well.
"It needs a little bit of time to adapt to the league. It's very different to Germany but I'm looking forward to it."
Havertz is one of a number of signings Lampard has made this summer, joining Hakim Ziyech, Timo Werner, Thiago Silva, and Ben Chilwell.