Gavin Swankie was impressive for Dundee on the left wing, where he gave Brian McLean, standing in for captain Paul Quinn, an uncomfortable evening at right-back.
"I said prior to the game that Gavin could play a big part. When he's on that form he's phenomenal for us," said the Dundee boss.
Despite the result, Rae was unhappy with referee Eddie Smith, who sent off Kevin McDonald and Gary MacKenzie in the last ten minutes of the game.
"I was getting a bit frustrated at some of the decisions. I don't understand how he could book the guy for the first one.
"The boy wasn't even looking for a foul. Anyone who knows Kevin McDonald knows he is not a tackler," said Rae.
Looking ahead to the Scottish Cup quarter-final tie in Dumfries against Queen of the South, Rae was in a positive frame of mind.
"It's a difficult place to go," he said. "We've lost a couple of players tonight, but it's an opportunity and we've got to go and try to progress."