Norgrove died in hospital on Saturday, nine days after developing a blood clot on his brain during his sixth professional fight against Tom Bowen at The Ring in Blackfriars, London.
Referee Jeff Hinds stopped the contest early in the fifth of the scheduled six rounds after growing concerned by the 31-year-old light-middleweight's behaviour.
Norgrove subsequently collapsed and was immediately taken to hospital.
"We are one of the strictest authorities in the world," Smith told BBC Radio 5 Live.
"This is an acute injury that can happen any time. He had his medicals done and had his brain scans done.
"There was nothing there of any concern whatsoever, otherwise he wouldn't have been in the ring.
"He was a fit young man but we can't guarantee an acute injury can't happen - no doctor in the world can guarantee an acute injury can't happen.
"We all know the dangers that boxing has, every boxer that participates knows the dangers.
"As a governing body we put in place all the medical provisions we possibly can, but of course these things still happen."
Norgrove, a former amateur and white collar fighter from Woodford Green, is the first boxer to die in a British ring since Scottish bantamweight James Murray in Glasgow in 1995.
The sense of tragedy was heightened by the fact that Norgrove was winning the contest after knocking down Bowen in the opening round and having taken little punishment himself.
"I've had reports over the last week and it wasn't a particularly hard contest," Smith said.
"He hadn't taken any particularly hard punches but the referee dispensed with the count, the medics were in there straightaway and he was in the hospital within 25-30 minutes.
"Procedure-wise, everything worked extremely well but this is the nature of the sport we're in.
"When asked [whether boxing is a legitimate sport], I say: 'What are you going to replace it with?'.
"Michael did this because he wanted to do it - every boxer that steps into a ring does it because they love it."