Kobayashi and his team-mates aboard the #7 Toyota GR010 Hybrid, Jose Maria Lopez and Mike Conway, finished a distant third as a result of damage sustained in the incident along Monza's start/finish straight with the Alpine A480-Gibson Matthieu Vaxiviere late in the penultimate hour.
Vaxiviere, Nicolas Lapierre and Andre Negrao survived the clash unscathed and went on to take a second win of the WEC season and extend their championship lead in the process.
Kobayashi was running side-by-side with Vaxiviere in the battle for the lead when he moved across on the French driver, the right-rear tyre of the Toyota deflating immediately as it touched the Alpine's front-left.
The Toyota team principal was able to get the car back to the pits for the tyre and damaged rear bodywork to be replaced, but the time lost and a subsequent 90-second stop/go penalty dropped the #7 car two laps off the lead, and behind the second-placed #8 machine.
But Kobayashi reckons that he was fighting a losing battle against the Alpine and that second and third was the best Toyota could have hoped for.
“We tried our best to get the win but it was not enough today and we missed the opportunity," commented Kobayashi. "Two cars on the podium is the best we could manage.
"In my stint, I struggled a bit in terms of pace. I tried to retain our position and we took a strategic choice not to change tyres at my pit stop. That gave us track position but I started to lose pace. Then I had contact with the Alpine so we had damage, lost a lap and then had the penalty.
"At the end of the day I don’t think it really changed our final position. We weren’t quite good enough today so we need more for the next race."
Third place at Monza leaves the #7 Toyota crew's title defence hopes hanging by a thread, as Kobayashi, Lopez and Conway now trail by 30 points with only two races left to go at Fuji and Bahrain.
"We want to win both world championships so we need to win at Fuji," Kobayashi added. "There is a lot of competition in Hypercar now so it will be very challenging, but this is great for the fans and we enjoy it.
"We still have a chance with both cars and we will not give up.”
The Le Mans 24 Hours-winning #8 Toyota crew of Sebastien Buemi, Brendon Hartley and Ryo Hirakawa faces a more manageable 10-point deficit to Alpine after finish second at Monza.
But Hirakawa, who was in the car for the closing stages and had a close call of his own with Vaxiviere along the start/finish straight at one point, admitted to frustration at the team's defeat by a margin of just 2.7 seconds.
It followed the #8 car coming back into contention after losing ground with a braking regen issue that hampered Buemi's stint.
“I am a bit disappointed to be second because I tried everything to get the win," said Hirakawa. "The team reacted really well to the issue which Seb [Buemi] had and thanks to their efforts we were not so far behind and had the chance to come back into the race after the safety car.
"I was always very close to the Alpine but I couldn’t quite make it, which was frustrating.
"We only have two races remaining and the next one is our home track. We have to finish ahead of the Alpine to win the world championship so the goal is clear."
