Peter Bonnington, who is Hamilton's race engineer, asked the driver during a late safety car whether he wanted to take on new tyres.
The 37-year-old chose to stay on the track, but the decision proved costly as teammate George Russell, who started in 12th and did decide to make a tyre switch, fought his way past Hamilton to secure a top five finish.
"In that scenario, I have no clue where everyone is, so when the team say 'it is your choice', I don't have the information to make the decision," argued Hamilton.
"That's what your job is. Make the decision for me as you have all the details and I don't. I rely on the guys for that, but today they gave the decision to me and I didn't understand it.
"When you are given that responsibility it feels like gambling and I don't like that. It was just a bit unfortunate."
Hamilton and Russell went wheel-to-wheel for the first time since becoming teammates at Mercedes.
Russell was instructed to let Hamilton go back into fifth following an illegal off-track move, but the 24-year-old did get his man on the very next lap.
Hamilton added: "George was on the best tyre to start with, and in hindsight maybe I could have started on the hard tyre. But he did a great job to recover from his starting position.
"He was fair and had fresh tyres so I was a bit of a sitting duck. I am waiting for a change in fortune, but until then I will keep working as hard as I can."
Russell, who has already amassed 23 more points than his counterpart, added: "Obviously you leave a bit more room when you're battling with your team-mate than you ordinarily would do.
"I was told I had to swap positions back and that was a little bit frustrating as I was catching the guys ahead. Fortunately we all came home in one piece."
Max Verstappen was able to win in Miami despite a late charge from Charles Leclerc. Carlos Sainz Jr took the last podium spot - his third podium of the season - while Sergio Perez finished fourth.
Next up on the Formula One calendar is the Spanish Grand Prix which takes place on Sunday, May 22 at the Circuit de Barcelona-Catalunya.