The Russian, who will race for Toro Rosso next year, had to endure a shortened FP1 due to fog delays and a red flag caused by a medical helicopter problem.
But he made it clear afterwards that getting any laps under his belt was a bonus as he ramps up his preparations for 2014.
"I was happy to have those 20 laps and enjoy them all, so no regrets," said Kvyat, who ended the session just two tenths of a second slower than team-mate Daniel Ricciardo.
"It would have been perfect if we could get one and a half hours of running, but it didn't happen. It's not a problem though."
Kvyat said he had no problems in getting comfortable in the car, and reckons the gap between himself and Ricciardo was reason to feel encouraged.
"It was really positive from that side," he said. "I was 0.2 seconds off Daniel. I don't know how hard he was pushing, but it was still relevant to see the gap on the time sheets. It was very positive.
"I wasn't going crazy out there. It wasn't like a qualifying effort, as I am not so confident with the car yet.
"I did only the young driver test with this car, so this is only my second outing.
"But when I did finish the session, it was a bit unusual to have to give the car to somebody else - as it would have been cool to carry on.
"But that is how it works - and it is just a question of going step by step. I just can't wait for next year."