Red Bull boss Christian Horner said Hamilton was guilty of "dirty driving" and questioned how he would sleep after the incident at Copse Corner that caused Verstappen to need hospital checks.
After the race was red-flagged and once Hamilton served a 10-second time penalty, the British driver went on to win his home grand prix and in doing so cut Verstappen's championship lead to only eight points.
"I've been giving my all this past week," Hamilton said afterwards. "Of course I always try to be measured in how I approach, particularly in battling with Max, he's very aggressive, and today I was fully alongside him and he didn't let me into space.
"Regardless of whether I agree with the penalty, I take it on the chin and I just kept working."
Verstappen was initially treated by medics at Silverstone but then needed to be taken to hospital.
"He's bruised, he's battered, but no broken bones. It was by far the biggest accident of his career," Horner said on Channel 4.
The Red Bull boss made his "dirty driving" claim just minutes after the crash, which saw Hamilton come up on the inside of the pole-sitter, only for their wheels to touch and Verstappen to suffer a crash that left his car a wreck.
"The penalty doesn't fit the crime," Horner said. "He's had no penalty because he's gone on to win the grand prix. It's a desperate move that you wouldn't expect from a seven-time world champion.
"It's just irresponsible and a sign of desperation and it's completely destroyed the car."
Horner said Red Bull would "consider our options" over a possible post-race protest after Hamilton celebrated a record eighth victory in the British race.
"I don't think Lewis can take any satisfaction from a victory like that because we were lucky today that a driver wasn't badly hurt," Horner said.
"I hope he can sleep well tonight because that's not good driving."
Horner suggested the crash could ramp up the excitement for the rest of the season, backing his young driver to come back strongly.
"He's fit, he'll recover quickly and he's mentally very, very strong," Horner said. "If anything it'll just make him more determined.
"It just raises the stakes. It didn't need to be like that because it could have been a great race between the two drivers today."