The scrum-half kicked 19 points to lead his team to a 29-23 win against the two-time European champions.
"We've been taking a lot of heat recently from people outside our camp," BBC Sport quotes him as saying. "People can write what they want about us. I've got a lot of belief in the players and the coaches.
"We played the same game plan as the first five games - we just did it with more accuracy and more control," Laidlaw added.
"It's always important to start well in the Heineken Cup and win your home games. I thought the boys were outstanding."
Edinburgh's next game in the competition will be against Perpignan away from home next Sunday.