Abafana Bes'thende came out 1-0 victors thanks to a late strike from substitute Mwape Musonda, after a game of many missed chances from both sides.
Larsen praised his players for the positive result, but voiced his respect for his opposite number in Johnson.
"We expected this [tough match]; I've got a lot of respect for this Platinum Stars team as well as Cavin [Johnsons]," Larsen told SuperSport.
"I think he's doing a great job, and we had to grind out the result today... We knew it was not going to be easy because they are a team in form.
"But, once again, our players fought for 90 minutes, and I think both teams are guilty of missing sitters."