Sean Everitt was left frustrated after his side put themselves in contention to beat the Bulls at Loftus Versfeld, only to collapse late on as the hosts rescued victory.
The Edinburgh head coach admitted it was a golden opportunity for his side to record a rare win in South Africa.
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He said: "We're not happy with our performance although we could have got the result tonight. I think it was a scrappy game from both teams. We certainly put ourselves into a better position in the second half, which was pleasing.
“We were behind on the territory stats at half-time, we only had 43%, and I thought the guys did well to pressurise the Bulls into 12 turnovers and to concede nine penalties. So the accuracy in our execution let us down tonight and I'm very disappointed with regards to that.”
Everitt's side did salvage a losing bonus point late on, but Everitt said that was of little consolation after the 22-16 defeat.
He added: "We came here to win and that was our goal. I know the Bulls have made a fortress of Loftus of late, but we honestly believe that we have a team that could have won the game this weekend.
"Unfortunately, we have to look at ourselves on this one. I think we beat ourselves tonight.”
The decisive moment game when Boeta Chamberlain kicked a 50:22 after the Bulls countered from their own line following an Edinburgh turnover, then took a quick lineout to put Canan Moodie over.
Everitt admitted his side must do better.
“Yes, it was disappointing, because I think we were building enough pressure at that stage of the game.
"To get stripped two metres short of the line and to concede a try from 100 metres is obviously disappointing, because I think if we had scored at that particular moment, we would have gone eight points clear, and that gives you a really good opportunity to win the game with 10 minutes left.
"We know that we can control the start-stop time, and we didn't do that.”
Edinburgh lost both Dave Cherry and Mark Bennett to early injuries, and Everitt said he was unsure how serious either was, or whether they would be available to play the Lions in Johannesburg next weekend.
“We don't really know the extent of it at this stage," the Edinburgh coach continued.
"Dave's in quite a lot of pain, going over his ankle. Mark Bennett seemed to have strained his quad, so we'd have to do medicals tomorrow morning and see how bad they are, and then hopefully fly in some replacements, should they not be able to play in the last game."
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