Sergio Cirio calmly converted a 98th minute penalty to seal the win after Baba Diawara opened the scoring with a deft near-post header during the first-half.
McGowan admits the dramatic victory was a morale-boosting win for the Club.
“It was a massive win for us and especially for the fans,” McGowan said.
“And the way we’ve been going recently for the team morale and a little bit of confidence.
“We’ve got a lot of young boys in the team that haven’t won too many games in their career.”
“It’s important we finish the season as strong as possible and try and repay some of the faith the Club and the fans have showed us over the year.”
The win against the Roar saw Adelaide move two points adrift of the ninth-paced Central Coast Mariners – ending a five-game winless streak in all competitions.
A victory over the Gosford outfit on Saturday would see the Reds jump off the foot of the table for the first time since Round 16.
McGowan said avoiding the dreaded ‘wooden spoon’ would serve as extra motivation to claim the three points.
“It’s nothing to be excited about, getting off the bottom of the ladder,” he said.
“But in terms of a pride aspect, it’s a massive game for us.
“We definitely don’t want to finish last and as a squad we think we’re better than that.
“It’s about showing a bit more fight and showing that we’ve got the pride to get this Club out of the situation we put it in.”
McGowan stated the Reds are desperate to finish the season strongly to climb up the league standings and salvage some pride.
“You saw yesterday (against Brisbane), we’re hardly going to chuck in the towel with the A-League as well,” he continued.
“If we can’t make the finals we want to finish seventh, and if we can’t finish seventh we want to finish eighth.
“The way this club is we’re too big a Club to be at the bottom, the squad has too much pride to be sitting at the bottom.
“I don’t want to go from champions to finishing last, so that’s a massive motivation within the squad and Club.
“We’ll fight and scratch as hard as we can to get ourselves up the table.”
Adelaide United will face Central Coast Mariners in Round 24 of the Hyundai A-League 2016/17 season on Saturday, 25 March at Central Coast Stadium. Kick-off is at 5.05pm ACDT.