Mercedes boss Toto Wolff confirmed that the decision had caught the team off-guard and that Rosberg's replacement has not yet been chosen - and Hamilton said he would leave it entirely up to Mercedes to find him a new teammate.
"It doesn’t matter who [they pick]. I'll race them, I'm here to race. Now the focus is obviously on next year and hoping for a better season," he said.
"I’ve never been a driver to request [in regards to teammates]. I know a lot of the other drivers - Sebastian [Vettel] and Fernando [Alonso] - make sure it is in their contract.
"I just always asked to have equal rights. As long we're treated fairly, it doesn’t matter who is alongside you. Of course, we've got great team bosses who I'm sure will choose the right people to be representing the brand."
"The better the driver, the better it is for me when I beat them"
Asked by Motorsport.com whether he would prefer a teammate who could push him or one he could easily beat, Hamilton said: "I’ve never needed a teammate to be able to push me. The better the driver, the better it is for me when I finish ahead of them."
Hamilton did say he was keen on having a teammate "equally as consistent" as the retiring Rosberg, in order to help Mercedes see off rival teams like Red Bull.
"You need someone with good values coming in and representing the team in a positive way, good work ethic and consistency, obviously, so we can those win constructors’ championships.
"Obviously, you've got Daniel [Ricciardo] and [Max] Verstappen who are very very consistent - so, in terms of challenging for constructors' titles, which is obviously the team's first goal, we need to make sure we have someone equally as consistent as what we had before."
On whether he wanted Mercedes to take his input in making a line-up decision, he said: "Honestly, I really don’t care. If they want to talk to me, they can talk to me about it.
"It should be someone who has to work well in the team. There will be stronger characters and less strong characters – and some drivers who take alternative routes in order to deal with competition.
"There will be good and better ones out there for sure - I will be more than happy to help with that analysis."
He added: "I'm interested to see who would want to be my teammate - and respect anyone that would want to."
Additional reporting by Jonathan Noble