The Blues could conceivably be without Drogba until mid-February after their top scorer completed successful surgery on his knee injury on Saturday.
"Drogba is a big player for Chelsea. They'll get by against smaller teams, but I'm sure the bigger teams will be glad he's away," said Keane after their defeat in London.
"Every club misses important players. Good teams will react in a positive way and that's when you use the squad.
"The bigger clubs have bigger squads and they can deal with that. But there's no getting away from the fact that Drogba is a big player for Chelsea."
Keane added: "If you're asking me if Chelsea will win the league then no, my money is still on Manchester United."