The hosts broke the deadlock in the sixth minute through Michael Dawson but were pegged back on the brink of half-time by a David Marshall own goal.
Robert Snodgrass put Hull back in front with a sensational free-kick in the 65th minute before Ross Barkley levelled things up six minutes before the end.
Phelan said: “It was a battling performance. I’m pleased with the players, they’ve come through another tough, difficult game and they’ve shown terrific spirit.
“Credit to all the players at this football club - they’re all putting a real shift in. They’re training hard, they’re listening and they’re learning.
“They’ve got everything to look forward to, which is to progress up this league, and we’ve got a real battle on our hands in the second half of the season, but I think we’re up for it.”
Everton defender Phil Jagielka was disappointed to see his side fall behind to Dawson’s early effort but was pleased with their response.
He said: “It was the worst possible start for us.
“You want to come to a tough place like this and keep them quiet. We conceded so early but we showed some decent resilience in the first half, created a couple of half chances and obviously were very fortunate to get the goal just before half-time.
“We started the second half really well but obviously in Snodgrass they’ve got a player with some ability - especially on free-kicks.
“But fair play to the lads. It was going to be hard to break Hull down again but it was a fantastic cross from Bainesy (Leighton Baines).”