The event, at the former RAF Charmy Down airfield about 3 miles from the city, began on Saturday night.
People living in places as far away as Bristol complained that they had been kept awake.
Avon and Somerset police said that even though officers arrived at the scene minutes after being alerted, there were already “many other people on site.”
Superintendent Ian Wylie said the force knew it was most likely a big rally this weekend, but he didn’t know where it might take place.
Once officials were called to the former RAF post, he said, it was too late.
“We got the call just after 11pm (BST) and were there in 10 minutes, however, all the scenes were ready and all the music was already playing with a lot of other people on the site,” he said.
“It has become for us to make any arrangement … because of the protection of these revelers, many of whom were drunk, many of whom were drugged, and the protection of the officials present.”
He said it was not imaginable to gather enough officials to disperse so many people at that time of night.
“We don’t have a permanent army waiting to deal with those problems,” he added.
In an earlier statement, Avon and Somerset police said that despite the closure of the technical lanes, officials still refused cars on Sunday morning.
Ch Supt Wylie said the music stopped just after 1pm on Sunday and that the site, despite everything, was removed 3 hours later.
Dulcie Walpole, a local resident, said that in addition to the noise problem, the arrival of a lot of cars also had problems.
“We had appointments this morning and we couldn’t get out of the lane, there were cars parked to the end and everything is blocked,” he said.
“All our neighbors called the police and complained and they don’t seem to have done anything.”
Tanya Rich, who lives in Weston in Bath, said the rave music, held near the A46, woke her up at 05:00.
“I heard that dull noise. It occurred to me that they had the car radio up and it stopped, but it kept working,” he says.
“I went to my local Facebook organization and everyone talked and complained.
“People said they might hear it as far as Longwell Green, even Kingswood.
“It’s so noisy. You couldn’t open a window.
Superintendent Ch Wylie would conduct an investigation into the organization of the rave.
“These are, frankly, egocentric movements of Americans who seemed determined to forget about Covid-19 legislation and all the fitness forums that were widely broadcast,” he said.
“They have caused a significant disruption to the other people in Bath and the area.”