Simeone: More to come from Griezmann, Lemar
Griezmann scored the only goal of the game in the 63rd minute at the Wanda Metropolitano Stadium and was substituted with 14 minutes to go, triggering a period of pressure from the visitors that Atleti were perhaps fortunate to survive.
The 27-year-old attacking midfielder is still seeking full match fitness after his World Cup-winning exertions with France in June and July, but Simeone is well aware of his importance to the team.
"Griezmann is [improving] his level," he told a news conference.
"It's clear we're looking [on the field] for a good player, he's a very important player for us, the moment Griezmann stepped off the pitch the team couldn't have any attacking situations.
"We had a lot of good players but we couldn't make any transitions. Then evidently with the passing of the minutes, we saw what had happened.
"We won in the end, so it's not easy to start, because to do well at the start of the season is always hard.
"It's clear that during the last 10 minutes we didn't play well and our opponent played very well."
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Lemar, signed from Monaco in June, played the full 90 minutes on Saturday and should prove to be a valuable acquisition, if he can replicate the form that fired his former club to the Ligue 1 title and the semi-finals of the Champions League in 2016-17.
"Lemar is an important player," Simeone said.
"We needed him, the team needed a player like him to do a better job this season. If he's closer to goal he'll create more dangers. I think he can give us more than he has given us.
"In the defensive part, in other areas he's been doing a very good job with not that many matches with us and I think he'll grow with the more matches, especially with the understanding of the footballers that are around him."