"We scrummed well this evening and the pack laid the foundation for what was ultimately a solid performance," Coetzee said after the game.
"They (the forwards) were able to apply pressure in the right areas (of the field) and that's why they (the Kings) gave penalties away, and we were able to convert that into points."
Cloudbursts before and during the match made for soggy conditions, but the Newlands pitch drained remarkably well to limit the effects of the wet conditions, and Coetzee praised the pitch condition.
"I must give credit to the way the Newlands pitch coped with the all the rain," he said.
"This must be the best field in the country. If it was anywhere else, the field would have been cut up by the action. At times, we even tried to move the ball, despite the underfoot conditions."
Despite the victory, Coetzee said it would be a tough task for the Cape outfit to reach the Super Rugby playoffs, but he remained optimistic about the team's chances.
"What has gone before (in terms) of results is in the past and there is nothing we do about it," he said.
"We can only sit back and watch the results. It says a lot for the (Super Rugby) product that outcomes can be so unpredictable and any team is capable of winning matches."
Stormers' skipper Jean de Villiers praised his side's ability to string together phases of play throughout the match.
"We managed to put attacking phases together on several occasions, so we were always in the game," said De Villiers.
"There was never a time (during the match) when I felt we were going to lose the match."
Meanwhile, Kings' director of rugby Alan Solomons was philosophical about the way his team performed.
"There was very little in the game and in the end the teams scored a try apiece," he said.
"We had a chance to score in the end, but we'll be feeling good about playing the Stormers again (in two rounds' time).
"Playing without Luke (Watson) and Demetri (Catrakilis) were big losses for us, and hopefully we'll be at full strength when we play the Stormers again."