Leclerc and Sainz lined up sixth and seventh respectively, but both lost positions to Mercedes driver George Russell and Haas man Nico Hulkenberg as they crossed paths in Shanghai's first corner complex.
Sainz was pushed wide in Turn 2 by an understeering Leclerc, who visibly struggled to get his tyres up to temperature, further illustrated by a huge moment for the Monegasque in the second sector.
While Hulkenberg was easy prey for both, Russell proved a tougher nut to crack. Leclerc finally passed him on lap 9, while Sainz had to wait for the Briton to pit before being released into clear air until the mid-race safety car.
"It was a bit of a crazy race. What we did at the start cost both Charles and I one or two positions and that cost us a lot in the race," Sainz said about the intra-team battle to Spanish broadcaster DAZN.
"Then we tried to follow the Mercedes, we tried to overtake him but he stopped and then we stopped, we put the hard tyres on very early.
"In the last stint, I had to go very long, but we still managed to hang on for fifth, which I think was the maximum we could do."
Ferrari was tipped to do well in Shanghai, but that didn't prove to be the case as it struggled for pace on the harder Pirelli compound.
"Honestly, we weren't very fast this weekend, when you qualify sixth and seventh there's not a lot of pace in the car," said Sainz.
"In the race, we expected to be better but we weren't, so clearly this is the circuit where we suffered the most.
"We need to check if we've done everything we could with the set-up and if not, it's time to work on the car because this type of circuit didn't go well for us."
"I just focused on getting to the end and making sure Russell didn't pass me on new tyres, and we managed to do that."
Earlier in the weekend Leclerc felt Sainz "went a bit over the limit" defending his position to his team-mate in the sprint race, before declaring the matter was cleared up internally.
Sainz is F1's highest-profile free agent on the 2025 driver market, as he is set to leave Ferrari at the end of the season following the Scuderia's signing of Lewis Hamilton.
