Each side emerged with a point from the contest at Vicente Calderon, with Didier Drogba and Sergio Aguero both grabbing braces.
Atletico, under new manager Quique Sanchez Flores, took the lead midway through the second half but had to rely on a last-minute equaliser to salvage a 2-2 draw after Drogba's quick-fire double.
But Asenjo thought that the hosts looked more likely to secure three points over the course of the match.
Chances"The team was up to the challenge against Chelsea and we dominated the entire encounter, enjoying lots of chances," he told Atletico Madrid's official website.
"If we play this well, the team will climb out of this situation in which we find ourselves."
After a troubled start to the season, Flores' side languish down in 18th place in the Primera Division table.
However, after the spirited performance against Chelsea, Asenjo thinks a turn around in fortunes will come soon, possibly starting with Saturday's derby against Real Madrid.
He added: "This good game was a turning point in our work. Now we're going to face a complicated match in the derby, but we now have the feeling that we're doing a good job."