Mercedes promoted Ricciardo Musconi, Hamilton's former second engineer, to the role of Bottas' race engineer.
Bottas won four races throughout the 2019 season and finished second in the drivers' championship, following on from a winless season at the Silver Arrows in 2018.
"You have to work hard to build a relationship of trust with your engineers, and with Bono [Peter Bonnington, Hamilton's race engineer] and the other engineers we have grown into a really good team," Hamilton told Auto Motor und Sport.
"Ricky is a very talented engineer so it's obvious that he wants to go places, and there was an opportunity on the other car. But I must have gotten more out of him than he realised, and vice versa."
In the opening four races of the 2019 season, Bottas won two races and held the championship lead before Hamilton took command in the midway point of the year.
Hamilton admits that he felt the effect of 'Bottas 2.0' in the early stages of the championship and believes it was partly down to Musconi's switch to the other side of the garage.
"If he suddenly works on the other car, he'll say 'Listen Valtteri, we did it this way and that way with Lewis'. And his team is now doing things very much like mine," he said.
"So I had to think again about how to go in slightly different directions to get more out. And when you've been close to 100 per cent, that's not easy.
I'm never quite perfect in the first races because I always try a lot of things with the car," he said. "Then when there's talk of Bottas 2.0 and after four races we are tied with two wins each, of course I notice that. I'm only human."