"I drank a lot of coffee" means the same as "I drank many cups of coffee", there is no negative connotation. It is OK that I drank a lot of coffee.
"I drank too much coffee" has a negative meaning, It means that I am not ok, i feel strange after drinking the coffee.
I ate a lot of cake but thats ok I feel great!
I ate too much cake and now I feel sick.
I play a lot of computer games but its ok, i still find time to do other things.
I play too many computer games, its not ok because I never have time to do anything else.