The Southampton boss and Arsenal chief Wenger exchanged words following the goalless draw at Emirates Stadium on Tuesday night.
Wenger had reportedly shouted at referee Lee Mason "It's always the same with you" with Koeman responding to the Frenchman: "No, it's always the same with you."
Koeman confirmed the incident had taken place as it was reported, but insisted it was all in the heat of the moment and that it would not affect his relationship with Wenger.
"What was written in the press was true, and that's all," said Koeman
"It's emotions in football and it happened, and we go on
"Do I regret it? If I talk it's what I mean, of course
No, I don't think (it will affect our relationship)
"It's always a little bit of emotions and he was very disappointed about the result because they had some good chances."
Koeman was named manager of the month for January following Saints' recent fine run.
They emerged from a recent sticky patch to collect three wins, without conceding a goal, before the stalemate against the Gunners.
Next up is a tea-time visit from a West Ham side lying one place, but five points, above Southampton in sixth spot.
"We hope to get more consistency, because that's one of our ambitions that we had at the start of the season, to have a more regular season," added Koeman.
"It's the Premier League and it's so difficult to get a good run, and to change it if you are in a bad run.
"We know what we have to do
The confidence is totally back in the team after the last few results.
"We have a big game against West Ham because it's still a gap between West Ham and Southampton, and we'd like to make that distance shorter than it is now."
Koeman is set to hand £4million January signing Charlie Austin his home debut
The striker scored the winner on his first Saints appearance as a substitute at Manchester United last weekend, but missed out at Arsenal with a knock.
Left-back Matt Targett is out with an ankle problem and midfielder Steven Davis remains a doubt due to a hamstring injury.
Source : PA
Source: PA