Cech started for Arsenal in the 2-0 home defeat against Manchester City in its first Premier League game under new manager Unai Emery.
The result could have been even worse when, after receiving a back-pass from debutant Matteo Guendouzi, Cech passed the ball straight out of play for a corner, narrowly missing his own right-hand post.
Leverkusen's English Twitter account responded by posting a video of Bernd Leno – who joined Arsenal from the Bundesliga club in pre-season – beginning a passing move that ultimately led to a goal, with the caption reading: "In case you were wondering how to play out of the back".
Cech failed to see the funny side, however, taking aim at Leverkusen in a post on Monday while also praising his current club.
Taking to his official Twitter account, the former Chelsea keeper wrote: "At Arsenal, we share important values which make us a big club, not only on the football side.
"Fair competition, professionalism and sportsmanship are the biggest ones you teach young footballers and it's sad to see when other clubs don't share the same values. @bayer04_en."
After Cech's response, Leverkusen issued a swift apology in a reply to the goalkeeper's message.
"Hi Petr. It seems our joke about wanting to see Leno, our former player, in action has been taken a bit more harshly/personally than intended," Leverkusen posted on Twitter. "It was only a bit of banter. We’re all for the values you’ve stated and wish you and your big club all the best. Nice 1v1 save on Aguero!"