The Italian driver was in the lead of the race for a handful of laps after the leaders all pitted while he stayed out on the medium compound.
Giovinazzi stated that it felt "great" to lead the race, but believes that he and the team extended his opening stint too long.
"We extended too long, the run on the mediums," Giovinazzi told media including GPToday.net. "Then I had a small touch with Daniel which broke my front left suspension a little bit.
"So after that it was a difficult race, but we achieved the best result that we could. P10 for me, P10 for the team. Good enough, so now just looking forward to Sochi.
"P7 was for sure the main target, to be in front of Norris. Now we need to be looking at what we could do better and improve the race."
Giovinazzi believes that with more experience, he will continue to improve and prove his worth in Formula 1.
The 25-year-old has finished inside the top ten at the last two races, while he was also set to score in Belgium before he crashed out on the final lap of the event.
"To be honest, I knew the speed was already there," Giovinazzi affirmed. "From Paul Ricard, compared to Kimi who is a world champion driver, I was always really close to him, a little bit in front, a little bit behind.
"The race was maybe an issue of the tyres, but it's coming better and better I think. We need to improve a bit more but I'm really confident that with experience over time, I will improve."