The Premier League side battled gamely in the first leg of their Champions League quarter-final tie at the Vicente Calderon, but they were denied a positive scoreline after Griezmann netted from 12 yards after Marc Albrighton was adjudged to have committed a foul inside the box, with replays suggesting that it took place just outside.
Leicester were aware that they could not afford a slow start against the Spanish giants, but it was one-way traffic during the opening stages as the home side threatened an early goal.
Somehow, Leicester survived the opening quarter of the contest and they came close to netting a surprise opener when a Christian Fuchs cross almost found the run of Shinji Okazaki, but it was not long before Atletico went ahead in controversial circumstances.
Albrighton cynically fouled Griezmann as he entered the penalty area but despite the offence taking place outside of the box, the referee deemed that it was inside, much to the frustration of the Leicester midfielder.
Schmeichel had saved penalties in both legs of the last-16 tie with Sevilla but on this occasion, Griezmann sent him the wrong way for his 24th goal of the season.
Leicester got through the remainder of the first half, with Albrighton firing harmlessly wide from 30 yards, but the closing minutes were tarnished as Atletico appeared to be trying to get Jamie Vardy - a yellow card away from suspension - booked with both Stefan Savic and Diego Simeone guilty of trying to pressurise the referee.
Just before the hour mark, Leicester were dealt a blow when Huth was booked for a late challenge on Griezmann, and it was a foul which means that the centre-back is suspended for the second leg.
As the game entered the final 10 minutes, Atletico were dominating possession but Leicester continued to frustrate them and both Carrasco and Torres were substituted as Simeone searched for a second goal.
A last-ditch intervention from Yohan Benalouane prevented Griezmann from tapping home, but that was as good as it got for Atletico as they were made to settle for just the one-goal lead ahead of the second leg.