Dundee head coach Steven Pressley tells BBC Scotland: "I was exceptionally proud of the way they played.
"We played so well in the first half and went in 1-0 down. I said to them in the dressing room 'there can be no hard luck stories tonight, we need to make sure we get what we deserve from the game'. They reacted brilliantly.
"There's been so much growth in them recently. We had a really good result against Falkirk and coming into this game, I stressed we hadn't recored back-to-back victories in 20 months.
"We had to own that, and change that. The players responded brilliantly."
Kilmarnock interim manager Kris Doolan: "A sore one for everybody, especially after taking the lead in the first half. I thought we scored a terrific goal, we were asking to be clinical when you get fewer chances. You need to be clinical and take them. We did, and at half time there's a lot of optimism.
"We spoke about driving home that lead, going for the next goal, making sure we're the team in the front foot. But then we didn't start the second half well enough, and obviously we lose that goal, which is a poor goal from our point of view.
"That gets them back in the game. It gets their tails up when really we wanted to hammer home the advantage.
"When you take the lead in these types of games, you should go on and win. It's not as easy as that. It's the Premiership."