Simeone's men will take a slender advantage to the King Power Stadium for the second leg of the quarter-final tie next week after Griezmann won and converted a controversial penalty for his 24th goal of the season before the half hour.
But it was the forward's all-round contribution that caught the eye before the break and forced a Leicester side who failed to register a shot on target throughout the 90 minutes even further on to the defensive during the second period.
"Griezmann is a fabulous player," Simeone told a post-match news conference.
"He is very complete. You do not know what position he plays in. He works in midfield, assists like a number 10 and finishes line a number nine.
"He is a player that knows this season finale is an important moment for him and he is assuming responsibility with the status he has."
Simeone praised his team's performance but also felt Leicester were probably satisfied to be taking a narrow deficit back home, where they overcame a first-leg defeat to dump out Sevilla in the previous round.
"It was a hard-fought match. It's a good win for us but the second leg will be difficult," the Atletico boss added
"It's all still to play for. We live from game to game. First we have to face well the match on Saturday [at home to Osasuna in LaLiga] and then tie is at 50-50. I don't think anyone we work with feels we are already in the semi-finals.
"We expect a fantastic night of football at Leicester - the English atmosphere, the fans on top of the pitch. It was a pure football night."
Atletico extended their remarkable Champions League clean sheet record at home to 16 shutouts in 18 matches, with goalkeeper Jan Oblak a virtual spectator, and midfielder Koke was pleased with the result.
"We have to be happy, we would all have signed for 1-0," he said, as quoted by Mundo Deportivo.
"We knew it was going to be a very complicated game, they were not going to back down.
"There we expect a different game because they have to attack us. They are the Premier League champions, a very complicated team. We're going to give everything there to go through."