The Tangerines boss saw his side miss out on clinching a return ticket to the Ladbrokes Premiership when Greg Docherty sealed a 1-0 victory for Hamilton in their play-off decider
The Accies midfielder's second-half strike at the SuperSeal Stadium booked the Lanarkshire side a fourth straight year in the top flight
But it consigns United to another 12 months in the Championship and raises serious questions about the club's future
The Tangerines' auditors previously admitted there was "material uncertainty" over the club's status as a going concern after suffering losses of Â£1.55million following relegation last year.
Under-fire chairman Stephen Thompson insists there is no danger of the club slipping into administration after securing a Â£300,000 loan from New York-based Scottish banker Alastair Borthwick.
But McKinnon was unable to offer any reassurances to worried supporters about the state of the club's finances
Asked about the consequences of failing to bounce back at the first attempt, the United boss said: " We'll look at that next week
I'll have to speak to the powers that be and see how the finances are."
But the former Raith manager says the club will face more disappointment if money is not made available from somewhere
He said: "We go again in the summer, I'll sit down with the chairman and we'll take it from there.
"We want to improve the squad, that is a must
I've used the same team for the last eight games and it was a game too far.
"It's an absolute must that we invest in the squad
We were light today and that cost us."
United had to play six play-off games after finishing the Championship campaign third but ran out of steam as they came up against Martin Canning's hard-working Accies
After a goalless draw at Tannadice on Thursday, McKinnon's team hoped they had enough energy to produce a spark in the return.
But Docherty snubbed out their hopes as he lashed home from 25 yards after 64 minutes.
United skipper Sean Dillon had to be dragged away from angry supporters at full-time, but McKinnon defended his men against the fans who accused them of not giving their all.
"We're all feeling very flat - it's a deflated feeling," he said after the match
"I couldn't have asked for any more from my players
They've given everything, I can never fault their efforts
"I just felt at half-time they were starting to flag a bit, the six games have caught up with them effectively.
"We didn't have that spark and looked like a team which was hanging in there with the energy levels being down.
"People get disappointed after games and they can vent it
I can assure them it wasn't lack of effort which has done us, it was lack of energy levels."
Hamilton had to cope without skipper Michael Devlin and Massimo Donati due to injuries, while Darian MacKinnon was suspended.
But Canning hailed his side's spirit as they fought for a win which sees them set a new club record for consecutive seasons in the top flight.
"When you are Hamilton Accies and in the Premiership it's never going to be plain sailing," he said
" We always get written off and you can sort of understand it when you look at the budget and the size of the club
"This is the first time ever Hamilton has been in the top league for four years in a row, so we've made a bit of history
"I thought we deserved it
There was a lot riding on this game and thankfully for us we managed to win and stay up."
Source : PA