"I have no issues with some guys going out for a drink and blowing off steam. It's a long tournament," said Smith on the eve of his team's crucial World Cup Super Eights game against England.
"We do have drinking rules. If the guys don't go over it and push the limits, that's fine with me."
Cricket South Africa chief executive Gerald Majola said in Johannesburg he would be leaving for the Caribbean on a fact-finding mission over the players' behaviour.
He has also sought a report from the team management about media reports saying South African fans had seen several team members "extremely drunk" in public.
The supporters reportedly called a South African radio station and said they encountered several players at a bar on Saturday night after the team's five-wicket defeat against New Zealand in Grenada.
"I will be leaving for the Caribbean and have asked team management to prepare a full report on the allegations to be ready on my arrival," Majola was quoted as saying Monday by the South African Press Association.
"I have been in contact with the team and they have assured me nothing untoward has happened. I will therefore wait for the report before I make a decision on further steps to be taken."
The South African skipper said he was sure the players were aware of the limits.
"We do have drinking rules which require the players to calm down two days before the game. We will deal with it if the guys go over the limit, said Smith.
"There are probably were a few guys who had a drink, but I don't know what being intoxicated is. We've been the quietest team in the World Cup, probably due to where we've been based."