Ciftci and Gary Mackay-Steven both missed penalty kicks against Butcher's men, who saw Tom Taiwo sent off in the second half, while a Jordon Forster goal on the stroke of half-time provided scant consolation for the disgruntled home fans.
Butcher was candid regarding his own side's failings after the match, while lauding the attacking quality of the visitors.
He said: "It was a difficult evening, that's for sure and I apologise to the fans. It was not nice to watch.
"There is a lot of hard work to be done but we know what we have to do and we need to get on with it. I would ask the supporters to be patient because it does take time and we need to work with these boys.
"Dundee United's ability and confidence showed through. We were beaten by a better team. When they are in that mood and allowed to play, like we let them, they can carve you open, and they did on many occasions.
"If you sit back and let them play then you are going to get killed. And they destroyed us.
"We were beaten by a far better team, there's no doubt about that. It could have been more."
Ciftci opened the scoring in the 43rd minute having earlier missed from the spot, but Hibs drew level through Forster to send the teams in level at half-time.
Gunning put the visitors back in front in the 56th minute but, having seen another penalty missed on the hour-mark by Mackay-Steven, they had to wait until seven minutes from time to finally kill the game off when substitute El Alagui netted their third.
Dundee United assistant manager Simon Donnelly praised the finishing of El Alagui, after admitting the second half had been unnecessarily nervous for the visitors.
He said: "As long it was 2-1 there was always the danger they could snatch an equaliser so there was relief when Farid made it three."
- Sports & Recreation
- Farid El Alagui
- Gavin Gunning
- Gary Mackay-Steven
- Nadir Ciftci
- Tom Taiwo