Sainz started fourth alongside McLaren's Lando Norris and briefly led the Suzuka race after delaying his second pitstop, instead extending his stint on the medium tyres.
That initially cost him track position as he was undercut by team-mate Charles Leclerc, Norris and both Mercedes cars of George Russell and Lewis Hamilton.
But with 17 laps remaining Sainz used his hard tyres, which were much fresher than the sets used by drivers ahead of him, to scythe through the order.
However, even with a helpful tyre offset Sainz thought a podium recovery was "not possible" until he saw the "mega pace" he had on the hard compound, which was helped by clouds forming over the circuit in the second half of the race to cool things down.
"I was hopeful of achieving a podium that in the end we managed to achieve, even if it was a very tough race, very strategic," the Spaniard explained.
"The track conditions changed a lot through the race. We went from a very sunny track that we hadn't had a weekend to a very cloudy track.
"The degradation went down a lot and you could push a lot more on the tyres halfway through the race.
"This changed the whole situation quite a lot. At one point, I thought the podium wasn't possible. But then with the new hard [tyres], the pace was mega and I could get back onto the podium."
Sainz was never under any illusion of being able to match his winning Australian Grand Prix performance, where even without Max Verstappen's early retirement he looked set to run the Dutchman close.
But as the gap at the top opened up on a circuit that accentuates Red Bull's formidable strengths, Sainz still felt confident Ferrari's race pace would be better than in qualifying, in which he was soundly beaten by both Red Bulls and Norris' McLaren, while Leclerc only qualified eighth.
"We kind of knew our race pace was better than our qualifying pace," Sainz added, having finished 20 seconds behind winner Verstappen and eight seconds behind the world champion's second-placed wingman Sergio Perez.
"Still probably not enough to go for a win, because obviously starting P4, and given how good the race pace of the Red Bull is, it's almost impossible to think about a win."
