Kompany turned home a Gareth Barry strike at the start of the second half to snuff out any hope of a Newcastle revival after Carlos Tevez - with his seventh in six games - and David Silva had put the hosts in command before half-time.
Yaya Toure increased City's lead before the end.
"Vinnie is important for us," said Mancini. "We played without him for 60 days, which was very bad for us, like when we lost Yaya Toure for a month. "There are some players that are very important and if they don't play for three, four, five games it is a big problem."
He added: "It is impossible we can win the title but it is important to finish the season well.
"We want that second place and to win the FA Cup semi-final."