The 27-year-old Italian dismissed two radio requests to let teammate Kimi Raikkonen past in the latter stages of the Istanbul race.
Raikkonen was running much quicker at the time of the order but Giovinazzi decided to maintain his pace rather than concede the place to the former world champion.
And it proved costly as Esteban Ocon, the man both Alfa Romeos were chasing for 10th place and the final point on offer, held off Giovinazzi by seven tenths of a second as he navigated his tyre-worn Alpine around the 58-lap race without any pit stops.
When asked about what happened, head of track engineering Xevi Pujolar explained it was a regrettable incident.
Speaking to Racefans, he said: “We asked to swap positions but then at this point also Antonio was starting to pick up the pace and he himself decided that he wanted to stay ahead. And maybe that situation, this couple of laps, potentially we could have been faster as a team.
“We needed one more lap to catch Ocon. For sure for the team that was not the ideal.
“I did not understand well why we could not swap at this point because also when we have got both cars then we can change it back depending on the situation.”
Lewis Hamilton’s Mercedes teammate Valtteri Bottas won the Turkish GP to claim his first victory of the season.
Red Bull’s Max Verstappen reclaimed the lead of the drivers’ championship with second place. He now sits six points ahead of defending champion Hamilton who finished fifth.
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