Griezmann converted a 28th minute penalty for his 24th goal of the season in Wednesday's quarter-final first leg, although replays showed he was outside the area when brought down on the break by Leicester winger Marc Albrighton.
Leicester manager Craig Shakespeare was understandably aggrieved by that decision but the France forward's all-round inventiveness during the first half forced him further on to the defensive.
The visitors failed to register a shot on target over the 90 minutes and midfielder Andy King replaced forward Shinji Okazaki at the interval, with Wilfred Ndidi dropping into holding role to marshal the mercurial Griezmann.
"We changed it, we had to sacrifice one of the forwards and put Wilfred deep in a 4-5-1," Shakespeare explained to BT Sport.
"In the first half Griezmann was getting in between the lines, getting in the pockets and causing us problems."
"This is one of the best teams in Europe and we've given a good account of ourselves. We know what we're about at the King Power Stadium and we know what we've got to do."
Leicester overturned a first-leg deficit against LaLiga foes when they beat Sevilla 2-0 at home in the previous round.
Their task would be a little more straightforward this time around if referee Jonas Eriksson had not erred so badly before the half-hour mark.
"It's disappointing, it's a key moment in the game," Shakespeare said. "The referee has to get that one right, you can't guess on those things.
"The referee has a hard job but it's the key decisions that you want correct.
"It's a good break [by Atletico] and we spoke about that beforehand, but we'd like a chance to defend the free-kick instead of defending the penalty."
Leicester were without captain Wes Morgan due to a back injury and face further problems at centre-back in next week's game after Robert Huth's booking for a second-half foul on Griezmann earned him a booking.
Planning ahead, Shakespeare booked Morgan in for some late-night fitness work.
"I've just told him in there when we get back to the hotel he's putting his kit on and going in the gym to do a session," he added.