Although his effort was just 0.329secs off Hamilton's one minute 14.411s pole time and 0.242s behind third-placed Verstappen, the Monégasque driver was left ruing an error he believed cost him only hundredths of a second.
He told Sky Sports F1: "I was actually quite frustrated after my fast lap because I lost a little bit of time in turns 14 and 15. I took the kerb in the wrong way and lost seven or eight hundredths.
"I was expecting to lose two or three positions because we are all that close that seven or eighth hundredths makes a huge difference. At the end, [we are] P4 and couldn't have gone P3. It wasn't enough today."
Had it not been for McLaren driver Lando Norris exceeding track limits and losing a time that would have been good enough for third, Leclerc would have dropped to fifth.
With Norris instead starting from seventh behind team-mate Daniel Ricciardo, Leclerc is excited to do battle with one of the Scuderia's historic rivals again this weekend.
"We need to push because Norris did an incredible lap time and the two centimetres where he went off track doesn't make him gain any time," he added.
"He has done a great job and McLaren is really pushing. It is going to be a good fight all across the year and we have to be ready for it and push."
Despite his elevated grid placing, Leclerc conceded it is unlikely the Ferrari will be able to challenge the trio of cars starting ahead on the grid.
"On tracks like this where we are only three tenths out on quali, it looks like we could but I have to say it is quite strange this weekend," he explained.
"We are all so close and especially so close to the top teams but it gives us hope for tomorrow, even though I think they have a bit more to come in the race."
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