It was the third game in eight days for Wellington, following wins over Central Coast Mariners a week ago and Melbourne Victory on Tuesday.
But Buckingham said fatigue didn't play a part in the disappointing loss.
"I don't think fitness was the reason we lost the game - it was a lapse in concentration, and in the 87th minute that's cost us."
The game looked destined for a scoreless draw until Jamie Maclaren and Brandon Borrello combined to bamboozle Phoenix centre back Andrew Durante, with Maclaren providing the finishing touch.
"A mistake unfortunately has cost us the game, but I wouldn't put that solely down to Andrew," Buckingham said.
"There's a lot of stuff that built up towards that. He's made one mistake, but it's not solely his responsibility for the loss."
There was little to separate the two teams for most of the match, he added.
"But I think we only had two on target of the 11 we created. They had 12 with six on target, and unfortunately one of those was in the 87th minute," Buckingham said.
"It's been a continuing thing this season - we need to make sure that the chances we are creating, we're finishing more than we are."
Wellington slipped a place down the ladder to sixth, and travel to Adelaide next weekend seeking to revive their fortunes.
They'll be without Italian centre back Marco Rossi, who collected his fifth yellow card of the season and will serve a one-match suspension.
Buckingham said the Phoenix have been preparing for such a situation, with both Dylan Fox and Ryan Lowry ready to slot in.
The only other question mark is over holding midfielder Vince Lia, who left the field in the 56th minute with a suspect hamstring, although the measure was largely precautionary.
