Two Dan Parks penalties handed Scotland a 6-3 half-time lead and put the hosts on course for just a second opening weekend win in 13 attempts in the tournament before he turned villain 24 seconds into the second half.
Charlie Hodgson charged down a Parks kick before applying the scoring touch. Owen Farrell converted and finished with eight points on his debut.
The television match official ruled against Greig Laidlaw, on for Parks, after 63 minutes, and for all Scotland's endeavour they could not breach the white wall of defenders as England returned home with the Calcutta Cup following a first win in Edinburgh since 2004.
Robinson said: "It seems a little bit like deja vu. We've been here before and obviously we're all bitterly disappointed about what's happened.
"Winning and losing Test matches is all about inches and those small margins.
"We've not been able to convert the chances again. We've got to be able to take those chances."
Robinson remains without a win over his compatriots in four attempts, with the perennial problems of numerous errors and a continual failure to find the try-line.
Robinson has seen his side score 20 tries in his 25 Test matches in charge, but none in the last four games, since the World Cup win over Romania in Invercargill in September.
Chances were there against England, with the ball turned over after Jim Hamilton's early break, Ross Rennie denied by Ben Foden's last-ditch intervention and a knock-on in support of Richie Gray preventing another score.
When pressed on the lack of try-scoring, Robinson added: "We look at ourselves. This is down to us and we've got to stick together.
"We've got to look at what we're doing as a group. I'm accountable for that.
"I know my responsibility there. I will keep looking at it.
"We're all accountable for this. It's a team effort that we're about.
"We're going to solve this together and we will continue to work in that way."
Foden appeared to stick out a hand as Rennie attempted to deliver a scoring pass to Mike Blair.
"Ross makes a great break and credit to the way that Ben Foden defended it," Robinson said.
"I think he knew what he was doing, as any good full-back would.
"He's got to stop us from scoring."
Robinson was frustrated with referee George Clancy's interpretation of the breakdown, believing England slowed down his side's ball.
He also felt aggrieved after Laidlaw's effort was ruled out, with Ben Youngs preventing the try.
Robinson added: "I've spoken to Greig, he said he got his hand to the ball and first touch. These decisions are about small margins.
"The law states you've got to get downward pressure and it looked like there was downward pressure.
"Greig was confident that he'd scored. I was pleased with the way that Greig came on and the way he ran the game. I thought he did very well."
Robinson now travels to World Cup semi-finalists Wales with a record of two wins from 11 Six Nations matches in charge, facing the prospect of another disappointing tournament.
Hooker Ross Ford, following his first Test as captain, summed up the mood in the dressing room.
Ford said: "We've been here before. There's not really much to add to it. We've created chances, we've just not taken them.
"In the latter stages we kept playing and got ourselves into good positions. We just didn't convert that pressure.
"We said in the changing room it's not what we do, it's the execution of what we do."
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