They threatened after just 23 seconds when television match official Nigel Whitehouse was called on to examine a frantic scramble for the ball over the Irish line, with the Welshman eventually finding in the visitors' favour.
And Scotland went on to create numerous other try-scoring opportunities, the best of which saw them squander a two-man overlap on the left when Brendan Laney launched a poor long-range pass which bounced harmlessly into touch.
It was a dreadful error which was nearly matched by wasteful finishing at various stages later in the match, leaving McGeechan furious.
"I'm very disappointed," said McGeechan, who is stepping down as Scotland coach after the World Cup in October.
"We had two or three opportunities in the first half which we really should have put away. It's such an advantage to get points on the board early.
"I'm pleased with the amount of chances that we made - we created more space out wide than we have done for a while - but we just didn't put them away.
"If we had taken our opportunities we would have put them under more pressure, whereas when they put us on the back foot they got something out of it."