Robert Snodgrass' injury-time free-kick at Turf Moor brought the Tigers a seventh point from a possible 12 - the kind of tally many had expected them to have collected by Christmas - after Belgium international Steven Defour put the Clarets ahead with a classy solo effort from 25 yards.
Phelan has faced significant adversity since taking over from Steve Bruce in the summer and has been a dignified centrepiece at an otherwise chaotic club, but a permanent contract remains a talking point rather than a done deal.
Buoyed by his first taste of 'Fergie time' as a number one - having served on the Manchester United touchline as an assistant when the term was coined - he laid out his mandate to the Hull owners.
"I've made it pretty clear I want to be in charge of this group of players
I think the players have made it quite clear too," he said.
"At one point I thought we were playing really well, we might win the game and then it's over to negotiations again...then at 1-0 down you think maybe not, maybe another week.
"But I'm sure things will get resolved
They probably will do, one way or another.
"We haven't fallen out or done anything drastic, we're taking it day by day and hopefully another week doesn't go by without it being resolved."
Burnley boss Sean Dyche, who has often beaten the drum for English managers, backed his opposite number's claim after the late sickener denied his team a second win of the campaign.
"It's for them to decide but Mike's a good football man, he's been around a long time and I've got a lot of respect for him," he said.
Despite that Dyche was keen to suggest that the notion of Hull as a crisis club did not quite reflect the strength of their first XI, which here included nine capped internationals.
"Don't be bluffed by this 'woe is Hull story', they have a lot of experienced players and some of those players cost a lot of money," he said.
"We are back in the Premier League and it's not an easy task
I thought we probably edged the game
It was tight but I thought we did just enough and probably should have seen the game out
"But it happens, we've done it to many others teams since I've been here."
Phelan gave the final word to Snodgrass, who scored in the opening day victory over Leicester and bagged a hat-trick for Scotland against Malta last weekend.
He missed Hull's last season in the Premier League with a career-threatening knee injury and is making up for lost time with aplomb.
"He went through a real spell where it was serious...would he continue in this game?" he said.
"He's worked really hard, now he's scored a hat-trick for the national team and a perfectly executed free-kick for his club in a week."
Source : PA
Source: PA