Coetzee's charges now tackle the Free State Cheetahs at Newlands on Saturday for a spot in the final.
"It was definitely a very pleasing result. I think it was a big improvement on last week. That's been our motto throughout the campaign - to improve on the previous game.
"The pack in particular played well. There were lots of physical intensity and a hunger to shut them out. The defence came back nicely as well. We made some big hits tonight and put the pressure on on the opposition.
"So I am pleased with the result. This team showed big character and responded to the occasion. But the job is not done yet, although I have to say I see something special in this team."
Coetzee was not happy with the finishing, saying the players let a few try-scoring opportunities slip through their fingers. He also said the team responded very well to what was said by the opposition coaches before the game.
"The game is played between the four lines and the team responded very well. We will review the game on Monday, but we left a few opportunities out there.
"I am still happy though. The pack played and scrummed well against a strong Sharks tight five. There is nothing more you can ask from a team when they play with that accuracy.
"The Boks in particular with the experience they brought to the side made some good decisions. The communication on defence was outstanding and that is what we need at this stage of the competition.
"But like I said, we have achieve nothing yet and we are looking forward to a home semi next week at home."
Coetzee said the only injury concern at the moment is Springbok centre Jaque Fourie. "He suffered a foot injury. We don't know the extent of the injury yet. He has to go for X-rays and we will know more about the injury by tomorrow."
He added that there would also be the normal bumps and bruises. "The collisions were of test match quality tonight. The hits were severe and hard and the physicality with which we pitched up was commendable, especially the tight five and pack. The old cliché is that it all starts up front."