Friday and Saturday qualifying topper Leclerc had launched cleanly to comfortably hold off front-row rival Verstappen into Turn 1 at the race start.
But the Ferrari driver was then left vulnerable as DRS was activated at the start of lap three of 51, with the chasing defending champion cutting the 0.4-second gap before using the overtaking aid to pass over the line.
A compliant Leclerc was then deposed to his eventual third place at the start of lap six, as victor Perez did similar to his team-mate by activating DRS to overtake on the inside run to Turn 1.
As Perez and Verstappen pushed each other in the battle for the win, Leclerc fell 21.217s behind the lead duo come the chequered flag, although he pipped fourth-placed Fernando Alonso by 0.8s.
This margin left Leclerc to declare that Red Bull remain in “another league” to Ferrari when it comes to race pace, with the Monegasque also having ceded the lead to Perez in the Saturday sprint race.
Leclerc said: “[Red Bull] are in another league once it comes to [the] race.
“Over 51 laps, it was just not possible. They have so much more pace than we do in race pace.
“I think they found something that we didn't yet. That's where our focus is at the moment, everybody's working flat out to try and understand what we can do in the races, especially to just get more performance.”
However, Leclerc did take some solace from the set-up tweaks made by Ferrari in Australia, which have unlocked more pace and have carried over to the competitive showing in Azerbaijan.
Asked if he felt the gap to Red Bull was narrowing at all, he said: “Honestly, the feeling is a little bit better. But when I see the gap, and I'm pretty sure that when you have this type of gap, you're probably not pushing 100%.
“We don't really know how much we have closed the gap. The feeling is a little bit better.
“But again, also the Aston Martin was really quick. today. So we still have a lot of work.”
Having kept Aston Martin’s Alonso at bay to end the two-time champion’s run of podium finishes in 2023, Leclerc added: “He was pushing.
“I knew what his intentions were at the beginning, because he always does that, trying to keep the tyres at the beginning of the stint and push at the end. So, I tried to do the same.
“And at the end, it was close, but not enough for Fernando today.”