Mercedes got its Silverstone weekend off to a bad start on Friday when Russell and team-mate Lewis Hamilton were only 12th and 15th respectively in FP2.
However, after overnight work, helped by a sim session that Mick Schumacher reported on social media that finished at 2:15am, the W14 was in much better shape on Saturday.
Russell and Hamilton qualified sixth and seventh behind the Red Bull of Max Verstappen, the two McLarens, and the two Ferraris.
"Yesterday after FP2 strategy had us down as 17th and 18th quickest in single lap work, and third and fourth quickest on the race pace,” said Russell after the session.
"So the only thing different between those two were the tyres. We made some really good improvements overnight. Frustrated to see we're only half a tenth from P3, that would have been an amazing result.
"But I felt happy with my lap. Lewis has been pushing me really hard all weekend, and I sort of stayed calm. It all came together on that last lap. And there's no reason we can't fight for P2, P3."
He added: "It's exciting these sessions, I think it makes it exciting for the fans, makes it tense from the driver's seat. But you've got to have faith in your team, faith in yourself.
"Fortunately, we did the majority of things right. I wouldn't say it was plain sailing through the session, Q2 was a bit tense. But we probably ended up where we deserve to be."
Russell also admitted he hadn’t expected McLaren to produce such impressive one-lap pace: "Exceptionally surprised by them. They've done an amazing job. Not too sure where all of that performance has come from, even last weekend. And their race pace was fast.
"That's going to be the interesting one tomorrow because you often see teams quick on a Saturday and go backwards on a Sunday. I have a sneaky feeling that won't necessarily be the case with McLaren. So we have a fight on our hands.
"I'm feeling positive, feeling motivated. But there's a couple of unknowns. I think we know roughly where Ferrari will be.
"I think we probably have a tenth or two on them, whether that's enough to pass them physically on track rather than around the pitstops. The McLarens will be in there."
Regarding Friday’s problems and Schumacher’s sim contribution, he said: “I think our FP2 pace was so slow because we didn't use the soft tyre in FP1. So we didn't really understand... We went in a bit blind.
"Mick and the team are doing a really great job with all of the overnight work. I mean, we've also got to give credit to the drivers who have been also doing the sim when it hasn't been Mick.
“And also in the previous years the drivers that have been working until 2, 3, 4 o'clock in the morning. Because that work is crucial.
“I think, as a team, we're one of the best with our simulations. And the simulator is state of the art, the best thing by far I've ever driven in terms of the virtual world, and it clearly pays off."
