Leclerc qualified third for the season opener and, having saved a new set of soft tyres, he was able to jump Sergio Perez at the start.
Later the Mexican got back ahead and Leclerc had to settle for third as leader Max Verstappen and Perez pulled away.
However, his race was ended by a loss of power that saw him stop on track on lap 40.
"It's not good enough," said Leclerc of Ferrari's race pace.
"We are far from Red Bull, so we need to push and understand what did they find during this break because they are on another planet on race pace.
"I mean, for now, we don't know. We are fast in qualifying, but we are not fast in the race, and it's not by a little.
"So I think Red Bull found something big somewhere, and we need to find that. It is very difficult to understand because obviously, the car from quali to race is not changing at all.
"But for some reason on one lap we are very close to them, and in the race we are a second away in some parts of the race. It's crazy, the difference, so we need to look into it."
Asked by Autosport if Ferrari had made the straight-line gains it had hoped for, he said: "Yes, but we are lacking in corners now."
Ferrari suffered from greater tyre degradation than Red Bull in the race, which was a regular characteristic during the 2022 season.
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The team explained then that degradation was exacerbated by the drivers having to push harder in races in order to keep up with the improving Red Bull, and Leclerc acknowledged that it was a similar situation last weekend.
"I think we are just slow," he said. "The tyre degradation may be a little bit, but eventually we just lack performance.
"We need to push more in order to extract the performance out of the car so then the degradation comes up. We need to look into it because for now we are really far from the winning race pace.
"I think it's very difficult to separate deg and performance. I think eventually we are just too slow in the race, and because we are too slow we are pushing a lot, and we are destroying the tyres, because we are slow.
"Red Bull seems to have so much more performance than we do in the race so they can manage in the first few laps, and then they start to push, and so that deg is much better."
Leclerc insisted that there was little positive to be gleaned from the Bahrain weekend given both the performance issue and the unreliability that struck his car.
"The only positive we can take away from the weekend is that we did the right choice in qualifying by keeping those new softs," he said.
"We had a good start, but that is definitely not enough to make me happy after what happened.
"We were in second place for quite a few laps, which honestly was the best we could hope for.
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"Then we got passed by Checo which was just a matter of time, they are in a league of their own this weekend in terms of speed, so we couldn't really challenge them. All of that doesn't matter, as we need to finish the race.
"It was all about trying to manage the pace, manage the gap with the guys behind, which I was doing, not really pushing massively, but anyway there wasn't time enough in the car to be able to challenge Red Bull.
"So third was the right position, but unfortunately, we didn't finish the race."
