Hamilton takes blame for Alonso collision on Belgian GP first lap
Alpine's Alonso had called the most successful F1 driver of all time an "idiot" who "only knows how to drive and start in first (place)" after the pair made contact while fighting for second.
Hamilton told Sky Sports television he did not care what the Spaniard had said.
"Looking back at the footage, he was in my blind spot and I didn't leave him enough space so it was my fault today," he said, apologising to the team.
Double world champion Alonso had lined up third on the grid, with seven-times champion Hamilton alongside.
Alonso made a great start to seize second from Red Bull's Sergio Perez while Hamilton moved up to third and tried to overtake.
They collided, Hamilton's Mercedes lifting high into the air and clattering across the kerbs before parking up beside the track - ending his record of finishing every race this year.
"What an idiot, closing the door from the outside," exclaimed Alonso over the radio.
"We had a mega start but this guy only knows how to drive and start in first."
Stewards investigated the incident and decided to take no further action.
They said video evidence showed Alonso was on the inside at turn five but Hamilton's front wheels were ahead of the Spaniard's at the entry to the corner.
"At no point did Alonso appear to lose control or understeer," they added. "Hamilton turned in towards the apex of the corner with Alonso still alongside and the collision occurred."
Hamilton, winner of a record 103 races, continued for half a lap before slowing and pulling over with smoke coming from the back of his Mercedes.
Alonso finished fifth, the best he had hoped for before the race, and struck a more conciliatory tone.
"He now saw the incident and he takes the responsibility, which is obviously very nice from him," said the Spaniard.
"It was a lap one incident, nothing really to say there...these things happen, especially in that corner. It happened in the past. I remember also with Lewis and (Nico) Rosberg, the same thing. It's a tricky corner.
"Luckily my car was very strong and nothing happened and I could continue. I felt the car OK for the rest of the race."
The stewards said the accident triggered medical warning lights in the car but Hamilton went to the medical centre only after Mercedes were warned they could face further action if he did not do so.
"This is not the first time this season that drivers (not Hamilton) have initially refused to go for a medical check," they added.
"The stewards issue a warning in this case, with a reminder to all drivers that stronger action may be taken in the future."