"I'm very disappointed because the scoreline flattered them," insisted the former British Lions coach.
"There were some very good performances from us out there. We let them off the hook once or twice when we could have scored and then we let them in for some soft tries.
"If we had picked-up a couple of tries, then the score would have been a better reflection of the match.
"There were a lot of good things to take from the game - our delivery of the ball out of contact was excellent and we got behind them in the first half.
"It was certainly a much better performance than our previous three games. But we defended too much and too readily in the second half. We should have been more proactive when we had the ball."
McGeechan refused to criticise referee Alan Lewis after the match official sent Andrew Mower and Simon Taylor to the sin-bin in quick succession.
Mower was shown a yellow card in the 12th minute for taking Mike Tindall out in the air, while Taylor followed him off the pitch a minute later for an early challenge on Josh Lewsey.
Despite being down to 13 men, Scotland rallied and even managed to add to the score with a penalty from Chris Paterson, who kicked all of his side's points.
"We should have played the whole match with 13 men because I thought we coped really well during that period," said McGeechan. "It was a credit to the players on the field.
"We ran the clock down for 10 minutes and kicked a penalty. You've got to think on your feet against England and I'm pleased to say we did that."