Sainz revealed after Friday's practice running at the Bahrain International Circuit that he was struggling to understand the Ferrari F1-75 car over the short runs, leaving him with work to do overnight.
But he bounced back in qualifying by taking provisional pole in Q3 ahead of Leclerc and Red Bull's Max Verstappen, only to slip to third during the final runs.
The Spaniard wound up 0.129 seconds off Leclerc's pole time, but felt pleased to have even been in the fight after struggling through practice.
"It's been a very difficult weekend for me, I've been slow, simple as that," said Sainz. "Charles has been doing a much better job than me all weekend, and I have been playing catch-up.
"Honestly, there's been points this weekend that I was very far behind, so by the time I hit qualy and I was fighting for pole, I was a bit more relieved.
"In the last lap, [Leclerc] did a very good lap. I think he put together everything, and at that point, you just need to congratulate and say good job to the team.
"It's great news to be fighting back in pole position, first time for me also fighting for pole. So yeah, quite interesting and exciting times ahead."
The 1-3 marked an impressive return to form for Ferrari, which has failed to win a race since Singapore 2019 after seeing its form slump dramatically in 2020, making last season one focused on recovery.
Ferrari had been tipped to start strongly in Bahrain after impressing through pre-season testing, but Sainz said the team had remained focused on executing everything perfectly, and would not be getting carried away with this result.
"We haven't believed at any point that it was going to be easy," Sainz said. "I think we did a very smooth quali, no mistakes. I think we need to keep it that way going into tomorrow. I see the team focused, confident, but not overconfident and not over-celebrating at all.
"We have the reality that we know we are Ferrari, this is back where we should be, and we cannot be too excited about it. It's obviously good news, and everyone will be happy today.
"But it's still a long way to go in the year, and it's only the first quali and first race."
