Robert Snodgrass equalised a minute later and Hull went on to win 3-1 on penalties on Tuesday.
Phelan said his players showed immense courage to stage such a fightback and got the result they deserved.
"On the night we performed heroically in the end and the players stuck to the task," Phelan told the club website. (www.hullcitytigers.com)
"We played against adversity at times, but we came through. We came from behind again and that is something we seem to have in our locker at the moment, although we'd rather not have to do it.
"We've put in an exceptional performance under a lot of stress. Ten men, extra time and penalties, we've gone through the lot.
"The players have put a lot of effort in and got a result, so I'm pleased for them."
Hull, who are third from bottom in the Premier League with 11 points, travel to Middlesbrough, who have a point more in 15th, for their next game.
(Reporting by Debanjan Bose in Bengaluru; editing by Ken Ferris)
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