The Briton had qualified ahead of Leclerc and remained ahead during the opening phase of the race, but fell behind during the opening pit phase as the Monegasque and Norris' McLaren team-mate Oscar Piastri conducted earlier pitstops to claim the undercut.
In an effort to chase Leclerc, McLaren conducted a swap between Norris and Piastri as the Australian's pace was slower, and Norris started to eat into the Ferrari driver's advantage.
With that gap whittled down to less than two seconds, Leclerc responded by pitting and made good use of his tyres afterwards to ensure that he could rebuild his buffer. Norris attempted to close Leclerc down again but lacked the time to do so.
Reflecting on the battle, Norris felt that it had not been entirely unexpected to come away from Melbourne with a podium, and felt that the pace he had over Leclerc meant that second was achievable.
"I think when you take the Red Bull out of it, I would say [it was not a surprise]. I think our pace has been good all weekend," Norris reflected. "We put things together very nicely yesterday and showed a good long run pace on Friday.
"So I wouldn't have said we had no chance. I didn't expect for us to be competing against the Ferraris today and I think our pace was not as good as Carlos's, but probably better than Charles'.
"Being honest, we maybe missed out a little bit on an opportunity to be P2 today. For us to say that, it's a good sign and I think it's a good positive for the whole team, a good boost."
Norris explained that the plan was for him to pit to undercut Leclerc around the lap that the Ferrari driver pitted, forcing a quick recalculation from the McLaren pit wall.
He instead stayed out another six laps in a bid to build up a tyre offset, but Leclerc crucially had track position and was over four seconds up the road.
"We didn't leave anything on the table, but the lap we were going to undercut, he boxed," the Bristolian recounted. "So, you have to go on off and then do kind of a different strategy. We were close in the second stint and, if I boxed, I think I would have undercut.
"I missed that opportunity. So you always think what if we did it one lap earlier, but it's tough to make all those decisions at the time. It can easily go wrong at the same time; there are always some consequences of doing so.
"I think we still did a very good job today. Uh, third and fourth for us as a team is positive and a good load of points, but [Ferrari was] clearly the better team and they have a better car at the minute."
