The JiR Team Scot Honda rookie started from the 13th spot on the grid, but a bad start dropped him to 18th by the first corner and 16th at the end end of the first lap.
However, the Italian recovered well. He was sixth by lap seven and making up ground on Suzuki's Loris Capirossi, whom he overtook on lap 20.
But in the last corner of the race he had a contact with the Tech 3 Yamaha of James Toseland and went wide while trying to hold onto his fifth place and had to let Capirossi, Toseland and Kawasaki's John Hopkins through.
"We didn't have the best start, but we ran a strong race," explained Dovizioso.
"Despite our poor grid slot I was able to go to near the head of the race, which was good. From the first corner I was last - I don't know why - but from there I was forced to attack on cold tyres. Obviously this was risky but I pushed very hard until I was in fifth position and ahead of Capirossi.
"After I made the pass I was tired and unable to pull away and I was also asking a lot of my Michelin tyres. I was ready to fight in last corner, but I was going a little too wide and was trying to accelerate when James and I touched each other and it moved my bike wider still and I lost grip. After this contact there was no chance to keep fifth and I ended up eighth.
"It's clear that I wanted to celebrate my 100th Grand Prix in a better way, but now it's important to work hard to improve our qualifying performance. The test here tomorrow will be important for this reason."
Dovizioso blamed his and his team's lack of experience for with regards to tyre choice and set-up.
"I have to say that we are still paying for our lack of experience," Dovizioso told Italia1 television. "Here too, we had a difficult weekend with our tyre choice and when trying to solve our set-up problems. We still need to understand this bike and get experience in the choice of tyres.
"Everything is new: more horsepower, more weight, and I don't have much experience to make these choices."
autosport.com