It appeared as if the Premier League club were heading out of the competition in extra-time when Newcastle took the lead, with Hull already down to 10 men after Dieumerci Mbokani was dismissed at the end of normal time.
However, the Tigers levelled through Robert Snodgrass and went on to claim a win on penalties, as Eldin Jakupovic saved two spot-kicks.
“On the night we performed heroically in the end and the players stuck to the task,” Phelan told the club’s official website.
“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 showed tremendous courage and spirit throughout against a very good Newcastle team that are serious contenders for promotion back to the Premier League.
“We’ve put in an exceptional performance under a lot of stress. Ten men, extra time and penalties, we’ve gone through the lot.”
Former Swansea caretaker boss Alan Curtis believes Carlos Carvalhal deserves great credit for the impact he has had at the club.
West Ham have issued life bans to five pitch invaders who came onto the playing surface in the defeat to Burnley last time out.
Brighton centre-half Shane Duffy says his game has come on leaps and bounds thanks to Chris Hughton and Martin O'Neill.
Bournemouth midfielder Lewis Cook says he is ready to take his chance with England should he be handed his senior debut.
Tottenham will have to make a massive offer to land Wilfried Zaha, according to former Crystal Palace chairman Simon Jordan.
Nigel Clough believes keeping Burton in the Championship this season will surpass the achievements of last term's survival.
Garry Monk has challenged his Birmingham players to maintain the high standards they set when beating Hull in their last league game.
Former manager Mark Warburton claims Rangers need to be patient with Graeme Murty or suffer the 'same old problems'.