The Pretoria outfit advanced to the semi-final with a convincing 45-14 win over Munster and Coetzee revealed a ton of work went into the game behind the scenes.
"A big win like this one is not just down to the 23 who played; it is the work behind the scenes that sets you up for a big performance," he said.
He also said their was extra motivation among the players to ensure their last game at Loftus this season was a good one to make it extra special for the players leaving at the end of the season.
"We wanted to make it special for the players who are leaving and probably played their last game at this ground - Ruan Nortje, what a warrior. He has served this team with distinction, Kurt-Lee [Arendse] as well. We wish them well in the future."
Coetzee praised the matchday 23 for making the most of their opportunities and putting Munster on the back foot every chance they got.
"We are super grateful to be through to the semi-finals, and a big thank you to the supporters who came out and gave us energy. We appreciate it," he said.
"We were clinical today, starting with the wings - Kurt-Lee Arendse and Stravino Jacobs - who won early scraps in the air to get us going.
"The forwards were very good in getting to the breakdown quickly, which gave us the platform to attack that we wanted.
"On Monday, the celebrations will be over, and we will reassess where we are. It will be a challenge going away, but this season we found our mojo with the travel - it pulls the group tighter. Glasgow is no easy task, but we will do our homework."