Last year's runners-up to city rivals Real Madrid, Atletico were unable to recover after conceding two first-half goals as their latest campaign in Europe's elite club competition got off to a disappointing start.
Atletico's Croatia forward Mario Mandzukic, brought in to replace the departed Diego Costa, was particularly wasteful, although he partially redeemed himself when he pulled a goal back for the visitors shortly before halftime.
"I thought the team attacked well," Simeone told a news conference after the game in Athens.
"They had some very clear chances in the first half but Olympiakos were efficient going forward," added the Argentine, who had warned against getting carried away after Saturday's 2-1 victory at Real in La Liga.
"Olympiakos were effective in front of goal and we were not with the chances we had. It was a difficult match, we knew that from the start."
Atletico will be looking to bounce back when they host Juventus in their second Group A outing on Oct. 1.
The Italian champions won 2-0 at home to debutants Malmo on Tuesday when Carlos Tevez scored his first Champions League goals for more than five years.
"Olympiakos now have a very strong foundation to qualify and now we have the uncomfortable prospect of playing Juventus at home, who are also in a good position," Simeone said.
"There is no need to get ahead of ourselves as there is still a long way to go in the competition."
Olympiakos made it to the last 16 of the Champions League last term and beat Manchester United 2-0 at home before losing 3-0 in the return.
The club's Spanish coach, Michel, who played for Real and Spain, noted that it was not easy to put three goals past Atletico, who only conceded three times in their six group-stage games last season.
"We suffered a lot because Atletico were fighting until the end but we are delighted," Michel told Spanish television.
"Everything came off well and we were effective in attack," he added. "This win was down to the commitment and great work of the players."
(Editing by Amlan Chakraborty)
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