The British driver switched to Mercedes from McLaren towards the end of the Formula 1 season, while Schumacher decided to retire from the sport.
"It's a privilege to be driving for a team that have had such a legend working with them and by no means do I feel like I'm replacing him," Hamilton told Sky Sports News.
"I think for me, I'm just younger and still have so much to aspire to do in the future. Of course, the team are expecting great results and all these kind of things, but that's good because that's what I live and breathe for."
The 28-year-old was officially unveiled at Mercedes' Northamptonshire base last Thursday.