The Jaguar driver felt that a podium at the very least was in the offing but was denied at the line by Rene Rast, who had defended third place despite running out of energy by the final corner.
Although Bird had mounted an earlier overtaking effort on the German, he went straight on at Turn 18 and had to concede the position back to Rast.
Following the safety car brought out on lap 28 for Nico Muller, who had crashed into the Turn 18 wall, the race was neutralised for two laps before restarting.
Only one lap was added back at the end and, at the late phase of the race, Bird had around 2% more energy than the cars ahead. He reckoned would have been enough to carry him above the cars in front had the race gone to a further lap.
Bird was seen talking in the post-race drivers' room to Sebastien Buemi, saying "if it had gone one more lap, for sure we would have won. I was flat-out for the last four laps."
Envision driver Buemi, who finished sixth, concurred that the race should have gone to a 41st lap, as did tenth placed-finisher Dan Ticktum (NIO 333).
Speaking to Autosport later, Bird said: "It was solid. Not the best, but solid.
"We should have got a podium today. Could've won today, to be honest; with the energy I had, I could have done it.
"But then the FIA didn't add the lap that they should have done, and then it became a flat-out race. And you can't overtake when it's flat-out.
"If they'd added an extra lap, I had the chance."
Bird - and Buemi, also using the Jaguar powertrain, behind him - both had useable energy in reserve, representing a turnaround from the first race where the Porsches were much more efficient compared to the other manufacturers.
PLUS: How Wehrlein's Diriyah double reveals Formula E's form book shake-up
The Briton explained that the energy saving was the result of Jaguar's work overnight, stating: "We've done a lot of work. We've done our homework and [this is] the result.
"I want it to be [a sign of things to come]."
