Hamilton started well down the grid after being forced to change his gearbox.
He roared through the field to finish on the podium behind winner Sebastian Vettel and Mercedes team-mate Valtteri Bottas.
Despite leaving Bahrain with a respectable points haul, Hamilton was left frustrated by issues speaking to his team.
"I started ninth so third is not bad at all," he said. "It's damage limitation, but I am happy.
"There were frustrating points in the race because the team couldn't hear me so I had to pick particular moments to speak to them.
"Communication is really difficult when you are trying to catch Sebastian, who is 25 seconds ahead, to know exactly what you need to do to not kill your tyres but make it so you catch him at the end."
Hamilton's latest gripe comes a fortnight after he was denied victory in Australia by a clitch in Mercedes' computer software.
The Brit racer also laid into Max Verstappen after the race, branding the Red Bull racer 'a d**khead'.
Vettel is now two wins from two in 2018.
"I think I came on the radio with 10 laps to go and said I had everything under control, but that was a lie as I had nothing under control," Vettel, who is now 17 points clear of Hamilton in the championship, said.
"Both Mercedes were strong at the end of the first stint and going onto the prime (medium) tyres they saw what we did and I thought that was Checkmate as we have to come in again."
Vettel admitted his victory was soured by an injury suffered by a Ferrari mechanic when he was 'run over' by team-mate Kimi Raikkonen.
The German said: "A bit sad because one of our mechanics got injured. A mixed day overall."
