Hamilton was left frustrated in the car as the Scuderia pit wall delayed a call on team orders in the second part of the race.
Hamilton lambasted the pit wall for its indecision, while Vasseur tried to claim that the team “did a good job” managing the situation.
Ferrari finished seventh and eighth in Miami with Leclerc in front of Hamilton, despite Leclerc being told to allow his teammate through.
The pair were on contrasting tyre strategies, with Hamilton on the medium compound in the second stint.
It saw him close in on Leclerc as the lead Ferrari battled with Carlos Sainz.
Once clear of the Williams, and with a pace advantage, Hamilton suggested the team swap the order and allow him to pursue Kimi Antonelli ahead.
Though that call was ultimately made, it took four laps.
“I lost quite a bit of the tyres in that,” Hamilton said of the delay.
“We were battling for position at the end of the day, but it would have been great if we could have maybe done what Valtteri [Bottas] and I did in Budapest years ago where, move, see if I can catch him, if I can’t, move back.
“Ultimately it didn’t work out.”
As the decision on whether to swap the Ferrari duo around was made, Hamilton fumed at his engineer, Riccardo Adami.
He was initially told to simply remain within DRS range, which Hamilton labelled “not good teamwork.”
After he was eventually told he’d be allowed to pass, the 40-year-old responded by suggesting the pit wall “Have a tea break while you’re at it.”
It didn’t end there.
Instructed to allow Leclerc back through after he failed to pull away, Hamilton was warned of the rising threat from Sainz.
“Do you want me to let him past as well?” he quipped.
After the race, Hamilton and team boss Vasseur discussed the matter.
“I can perfectly understand the frustration,” Vasseur acknowledged.
“They are champions, they want to win races.
“We are asking them to let the team go. It’s not easy. It’s never easy and I didn’t see another team to do it today.
“That’s why we took the responsibility to do it because it’s the policy to the team.
“We are racing for Ferrari first and honestly I think as a team we did a good job.”
Hamilton added that he told his boss to calm down during their exchange.
“Fred came to my room. I just put my hand on his shoulder and like, dude, calm down. Don’t be so sensitive,” he said.
“I could have said way worse things on the radio.
“You’ve got to understand we’re under a huge amount of pressure within the car.
“You’re never going to get the most peaceful messages coming through in the heat of the battle.
“It wasn’t even anger,” he added.
“It wasn’t like, effing and blinding and anything like that. It’s like, make a decision!
“You’re sitting there on the chair, you’ve got the stuff in front of you, make the decision, quick.”
Hamilton asserted that he will not apologise for his behaviour over team radio.
“I was like, come on guys, I want to win,” he said.
“I’ve still got my fire in my belly. I could feel a bit of it really coming up there.
“I’m not going to apologise for being a fighter. I’m not going to apologise for still wanting it.
“I know everyone in the team does too, and I truly believe that when we fix some of the problems that we have with the car, we’ll be back in the fight with the Mercedes, with the Bulls.
“It just can’t come quick enough.
“We’ll try something different in the next race, we’ll keep working on the processes.
“I look forward to a time when maybe I can fight for a podium. That would be nice.”
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