In Thursday evening's second free practice session, which is held in similar conditions to qualifying and the race, Lewis Hamilton led a Mercedes 1-2 ahead of Russell, with Aston Martin's Fernando Alonso in third.
Overwhelming favourite Max Verstappen was sixth as Red Bull put more emphasis on long runs.
And while Russell admitted Mercedes' progress compared to testing "exceeded expectations", he thinks Red Bull is still a cut above on race pace.
"We're not getting carried away with ourselves. The qualifying pace looked really strong, we still need to understand why it was so good," Russell said.
"We made some changes from the test and it exceeded expectations. But ultimately, the long run pace is where it all happens and Max is still ahead of us.
"It was very close with Fernando, Lando [Norris] and the Ferraris, Lewis and I were very similar as well, so we have a real fight on our hands.
"In race pace we were very pleased with the day, the car is performing really well but we're not going to get carried away with the timesheets just yet."
Mercedes' one-lap pace does provide it with a glimmer of hope that Red Bull isn't "out in the distance", as Hamilton phrased it last week.
"I hope so," Russell replied when asked if Mercedes now looks much stronger in qualifying trim than last week.
"We need to sit down and understand where this increase in performance has come from, whether it's a one-off, whether we can sustain this and what we need to do to fight for a serious position on Sunday.
"After testing Max looked a long way out in front, now that gap has reduced, but he's still out in front. I think he's still got a healthy margin to the others, rather than just a ridiculous margin to the others.
"So, by no means does this mean we're back, or we can fight with them just yet."
Hamilton added he was "shocked" by Mercedes' one-lap pace and progress compared to the pre-season test, but equally admitted his long runs wouldn't be enough to keep up with Red Bull.
"It's a shock to see us where we are but we'll take it for now," he said. "But we can't get ahead of ourselves, we need to keep our heads down, keep working on the set-up and trying to extract more.
"I think a long run pace is nowhere near the Red Bulls, for example, so we've got some work to do that."
When asked if a podium is on the cards, he replied: "I think we're going to be in the mix.
"It's a bit too early to say, but I think we're there or thereabouts with Ferrari and Ferrari and maybe Aston and McLaren.
"It's going be a close, a nice battle. [But] if Max is in the front, he will veer off as he has done for the last couple of years."
