The result snapped a three-game losing streak for the Reds but this win put them clear in second place and it was the way they achieved the result which satisfied the Dutchman the most.
"We are real happy we won the game today, especially a home game, but personally I'm more pleased with the way we did it," Coolen said.
"I was not surprised because I know my team can play football well. In this period we didn't have so much confidence after losing in the last couple of weeks, but we spoke about it that it isn't necessary.
"As long as we believe in each other and create some chances and play football, of course it doesn't mean you will win every game but at least you can start playing football, which is something we do well.
"It was more than good, it was well organised, we controlled the game, didn't give a lot away, created chances and the most important thing was that after a lot of games and a lot of travel, you have to keep the ball towards the end of the game and that's what they did, so that's a big compliment to them."
Adelaide next meet league leaders Brisbane Roar at Hindmarsh Stadium on Sunday in an enticing top-of-the-table clash.