Former Argentina midfielder Cambiasso, who joined Leicester in August having previously represented the likes of Real Madrid and Inter, was powerless to prevent Southampton from claiming an 11th victory in their last 12 matches in all competitions on Saturday.
Shane Long's brace secured another three points for Southampton, who remain second in the Premier League having displayed superb form in Koeman's first season in charge.
After the match, the Dutchman revealed Cambiasso had been impressed with Southampton's performance.
"I think we played on a very good level," said Koeman.
"Esteban Cambiasso said to me today, 'What a good team you have' and that's a very good compliment from a great player.
"The lads are doing fantastic. It's amazing how they work every day.
"It's really a team and the last few weeks maybe the wins are more difficult but we are Southampton, not Chelsea or [Manchester] City that maybe sometimes they win fairly easily.
"We have to fight. We know our qualities and that makes the difference. We've played only 11 games but I don't see a lot of difference between ourselves and the big clubs.
"I don't watch who is behind us. We have our focus on the way we play."
Southampton were forced to substitute Steven Davis in the first half against Leicester, but Koeman is hoping the midfielder will be available when the club face Aston Villa after the international break.
"He had a feeling in his hamstring," the manager added.
"I am hoping it will only be one or two weeks but we will have the scan tomorrow [Sunday] and then we will know more."
