A stunning strike from Hakan Calhanoglu condemned last season's Champions League runners-up to a 1-0 defeat in the first leg of their last-16 tie in Germany.
Fernando Torres had a goal disallowed in the second half and Tiago was sent off late on for two bookable offences on a night to forget for the La Liga champions.
Given that Atleti were also forced to substitute both Guilherme Siqueira and Saul Niguez in the first half, Simeone feels his side can consider themselves fortunate to trail by just one goal.
"It could've been worse. It was a strange game - I don't think either side created many chances," he said after the match. "We couldn’t handle their pressing. They won the second balls.
"I imagined Torres would have a chance like the one he had, which was ruled out by I don’t know who – the fourth official, the fifth, the third?
"Having made two changes in the first half, having had a goal disallowed and losing 1-0, I'm happy.
"I have the feeling that they left us with life because another rival may have pushed us harder."
Despite the double injury blow, Simeone refused to criticise Leverkusen for their tough-tackling style and is confident he has the squad depth to cope with any absences in the second leg.
"They're an intense team. We like playing against teams like that," he added.
"There is no problem. [Jose] Gimenez and Mario [Suarez] will likely play instead."