Hamilton had spent the race ahead of Russell until a late Safety Car allowed the Mercedes newcomer to have a pit stop with a smaller time loss than usual.
That quick stop elevated Russell ahead of Hamilton, which soon became a podium finish when Max Verstappen's Red Bull car hit trouble.
In the closing stages of the Melbourne race, as he was running just over a second behind the other Mercedes, a curious radio message was broadcast from Hamilton on the TV coverage.
Hamilton, who finished fourth, said: "You guys have really put me in a difficult position."
F1 driver radio messages are often broadcast out of sync with when they happened and sometimes lack the context of the rest of the conversation. This one was not accompanied by any of the preceding conversations Hamilton had with the Mercedes pit wall.
After the race, Hamilton claimed it was in reference to being told he needed to drop back and run in clear air because his engine was overheating.
"Basically, I couldn't race for position because the car was overheating, so I had to back off," Hamilton said.
When asked to clarify it was not a reference to being behind Russell, he just replied: "Because the car was overheating."
Despite his frustrations at not being able to finish on the podium, Hamilton felt buoyed to see how Mercedes had turned around such a difficult weekend.
"It's an amazing result for us as a team. It's such a positive," he said.
"We were over one second off on Friday, and it wasn't looking spectacular at that point. We did some great work overnight to qualify on the third row and then a great start. I was up in third and it felt great to be fighting, or to feel like we're fighting for a podium in that moment.
"Obviously we couldn't hold with the pace of the Red Bulls. Whilst we haven't necessarily improved the car over these three races, I think we've really extracted the most we could points-wise. From my side, I let the team down in the last race and didn't get the points, but to come away with this result is great."