After running third in the opening stages of the race at Albert Park on Sunday, Hamilton dropped back to fifth when he was overtaken on track by Sergio Perez and lost a place to Mercedes teammate George Russell in the pit stops.
Russell and Hamilton moved up to third and fourth when Red Bull's Max Verstappen retired while running second, leaving the two Mercedes cars separated by just one second for the final podium position.
While following Russell, Hamilton radioed the pit wall to say: "You guys put me in a really difficult position."
Hamilton ultimately finished the race in fourth place, but clarified afterwards that his radio message was related to his car overheating and not a criticism of the team.
Mercedes motorsport strategy director James Vowles has now explained the cooling difficulties Hamilton was facing that sparked the message amid higher-than-expected temperatures on race day in Melbourne.
"That was all about engine cooling and keeping the power unit cool during the course of the race," Vowles said.
"We push everything to the limit, as you would imagine, and one of those is engine cooling, and you do that by closing up the bodywork or changing the louvre design at the back of the car.
"That decision is made on Saturday but obviously we are racing on Sunday, 24 hours later, and in this particular circumstance, the ambient was one or maybe two degrees warmer than we had expected.
"As a result of that ourselves, and not just ourselves, you would have heard it from teams up and down the grid, were right on the limit of what the engine and the PU can take in terms of cooling requirements.
"During the course of the race, when you are following a car, it meant that Lewis had to compromise what he was doing. He had to move out of the dirty air of the car in front of him and make sure he got cool, clean air through the radiators to drop the PU temperatures down.
"But doing that makes racing the car in front incredibly difficult, and that's why his message came out."
Russell and Hamilton's run to third and fourth helped Mercedes keep second place in the constructors' championship ahead of Red Bull, which scored points with just one car after Verstappen's retirement.
But Mercedes has struggled to compete with Red Bull and Ferrari for outright pace so far this season as it continues to combat the porpoising problem on its W13 car.
Although Hamilton and Russell were both able to battle the Red Bull of Perez at points during the race, Vowles outlined how Mercedes was still trailing the front-running outfits.
"In terms of where we were in Melbourne, we have to face the reality: we were a second down in qualifying relative to Ferrari and in the race, Leclerc was in a league of his own," Vowles said.
"Bahrain ended up being still to this point in our season our most competitive race, as an example, as a gap relative to the front.
"Every race though that we move forward, we have a plan of action of what we need to test, try and develop on that car and I am sure all of our competitors have the same thing.
"But the key is this: we have to start clawing back that gap to the front."
