Leicester City came back from 2-0 down to draw with Southampton at the weekend.
Mane went through on goal when the Saints were 2-0 up, but he did not finish the opportunity, and the miss proved costly.
Leicester scored twice through Jamie Vardy to claim a point from the fixture, and Koeman was left frustrated with his side's lack of ruthlessness.
“We had the best chance to kill the game from Sadio,” he said. “After dribbling round the goalkeeper you at least have to shoot on target.
“If you get that opportunity you have to kill the game but at 2-1 it was more difficult. Maybe they were more fresh at 2-1."
Southampton's failure to win against Leicester leaves them in eighth place in the Premier League table, but they will still be relatively pleased with their start to the campaign.
Koeman's side struggled over the opening few weeks of the new term, but they have clicked into gear in recent weeks and are in a good position now.
Southampton have lost just one of their last seven matches and, despite his miss, Mane has been in fine form recently.
The Senegalese attacker has netted four goals in as many games, and he will be hoping to get back on the scoresheet at the weekend, when Southampton take on Liverpool.