The Prema driver started seventh before charging through the field, taking second by passing both Caio Collet and Jonny Edgar into Turn 1 on lap 15.
He closed in on polesitter and race winner Colapinto and was just 0.4s behind him by the chequered flag.
But Bearman says he thought he had an extra lap left of the race distance, and told his team over the radio he wished he had been informed to get a move on.
Speaking after the race, the Briton said: “I was kind of driving like I had one more lap, because I thought the last lap was the penultimate lap.
“So I just wanted to get close, within half a second, so I could pass him into T1, and I did that but then the chequered flag came out and that was the end.
“It was amazing, one of the best cars I’ve had this year. It’s really good.
“I was just able to push like hell and have mega pace and moves came off.”
Asked how his “big moment” at Lesmo 1 affected his fight for the win, Bearman added: “I was pushing, it was my first lap through Lesmo in the clean air, and the balance changes massively from when you’re following a guy to when you’re in clean air.
“So yeah, had a big moment but in the end it didn’t really change much because I wasn’t giving everything in those last laps because I thought I had one more.
“So I don’t think it affected much in the end, I still managed to keep the rear tyres in the window so it didn’t change much.”
Bearman now sits third in the standings, just 13 points behind championship leader Victor Martins and seven behind second-placed Isack Hadjar.
Despite the small gap, the Ferrari Drivers’ Academy member insists he would need “a miracle” to take the title.
Bearman said: “I think I have to hope for a miracle to win for the championship but I’m just going to do my best and show a good race.
“Today was a good performance, I think after Zandvoort it was going to be hard to win the championship, but I’m just going to do my best job and not think too much about it.”
He added: “I think it will be a messy race like today, I just need to try and stay in the points. I think we had good pace today but low risk, just score good points.”
Bearman will start from sixth in Sunday’s feature race, with fellow title contenders Zane Maloney, who is fourth in the standings, and Roman Stanek, who sits fifth, lining up second and third.
Martins will start fourth, with Arthur Leclerc in fifth. Hadjar lines up in 16th after a crash in qualifying damaged his title hopes.
