Parker gave his side a fighting chance with a well-taken equaliser in the first half to bag his fifth goal of the season, before they went on to win 2-1 at the FNB Stadium.
The former Bafana Bafana striker raised his side's performance, but felt they could have done better in certain areas as they now target eight wins from their remaining eight games in the title race.
"This as a game of small margins. I think I deserve this – I did my job, especially with the help of my teammates," he told SuperSport TV.
"We pressed well in certain areas but we should have been a little bit more ruthless up front, in trying to kill the game early.
"We realised that Sundowns are a ball-playing team so we looked good on the counter. We should have had a little bit of patience and could have improved on decision-making going forward.
"But we continue, we soldier on. From the last eight games, if we can win all of it we'll see where we stand at the end of the season."
Chiefs now move to second on the log standings, just two points off leaders Bidvest Wits, who have two games in hand.