Anderson said he had spoken to umpire Marais Erasmus as Australia's fast bowlers launched a furious pace assault during the second innings as England were skittled for 195 on the way to a resounding 10-wicket defeat at the Gabba.
"I mentioned it to umpire Marais Erasmus, but he didn't think it was too bad," Anderson told the BBC.
"I don't know what constitutes dangerous bowling. It's the umpire's personal take on it.
"I was batting with Jake (Ball) in the second innings and he got bowled two short balls from (Pat) Cummins that went over the shoulder.
"There was a third very close and wasn't given and I questioned when does it get dangerous.
"Marais said he was happy with it at the time. It's down to the umpires."
Umpires can penalise the bowler with no-balls and remove them from the attack if they judge their bowling as likely to cause injury based on the batsman's skill level.
Australia used short-pitched bowling to rout England's tail-enders throughout their 5-0 whitewash in 2013/14, a tactic skipper Steve Smith said his bowlers were using as a "blueprint" for the current series.
After Australia wrapped up the win at the Gabba, Smith was pleased that his pacemen were able to tear through England's tail and said the tourists could expect more of the same in the remaining four tests to come.
The second test, the first day-night Ashes match between England and Australia, starts at Adelaide Oval on Saturday.
Anderson was preparing for another pace blitz at the tail.
"We have to plan to get a barrage, which we are doing," he said.
(Writing by Ian Ransom; Editing by Greg Stutchbury)
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