The Swans had almost 70 per cent possession and had threatened to run away with during an opening half-hour when Villa were all at sea.
Michu, Graham and Wayne Routledge - who had given his side an early lead - were among those to miss gilt-edged chances at the Liberty Stadium.
Laudrup said: "We did not win because we only scored one goal from seven chances with that first-half performance. It was a great performance - it could have been 4-0 after 12 minutes - but we know how it is when you don't take chances.
"It means one mistake, one free-kick, one corner or whatever it is and the game is back level and that is what happened at the end of the first half. They had only been near our goal two or three times in the first 45 minutes and we gave Villa belief they could come from behind and get something out of the game.
"If we had got a second or third we would maybe be sitting here talking about a 5-0 win."
Laudrup was also disappointed his side were not awarded a penalty just before the hour mark.
Joe Bennett was penalised for handball on the left-side of his own area as he blocked Angel Rangel.
But referee Mark Halsey only awarded Swansea a free-kick on the edge of the box when the ball had appeared to strike Bennett just inside.
When asked if he thought it was a penalty, Laudrup said: "Yeah of course, both of his feet are on the line and the hand is inside, I think the line is still part of the box so there was no doubt about it. It was a clear penalty but it was not given and that's that, we have to go on."