But Shola Ameobi equalised and a Richard Dunne own goal put Newcastle on course for an unlikely win before Stephen Ireland salvaged a late equaliser.
Kinnear initially said he would only stay at the club until new owners were brought it, but he now has a taste for life at St James' Park.
He told Setanta Sports: "It's up to the people that come and buy it but of course I do (want to stay).
"I'd like to hang onto it for as long as possible. It's probably the best club I've worked at and I want to make the most of it."
Kinnear had nothing but praise for his players after they matched big-spending City for long spells despite being a man short.
"It was a fantastic performance from 10 men," Kinnear continued. "I couldn't ask for more. We were totally committed, played some decent football and created more of the clear-cut chances.
"I thought we'd just about hold on but there were a lot of tired legs. The good thing was we didn't get beaten and we've come out of it with a lot of credit and a point."