"We are absolutely over the moon," said Laidlaw.
"The players put in a great shift out there."
"We struggled in the first half with 13 men but we managed to stay in the game and I think that won us the game.
"Toulouse are a great side with great players and we were certainly worried when we went down to 13-men because it is hard enough to play them with 15 men , but we defended well and slowed the game down.
"Then, we got our boys back on and that is what probably one us the game. We were jogging off at half-time and they were walking and we knew we had to keep the tempo high and that is how we like to play the game.
"Hopefully, this is the pick up Scottish rugby needs. Glasgow are going well in the Pro12 and we are now in the semi-finals of the Heineken Cup. I think the crowd we had showed there is the support out there for us for these big games."
Edinburgh will now face the winner of the Munster versus Ulster quarter-final on Sunday in a semi-final at the Aviva Stadium in Dublin.