Having already qualified for the knockout stages prior to the match in Russia, Atletico rested four players but still appeared on course to seal all three points following Adrian Lopez's second-half strike.
A mistake from Thibaut Courtois allowed Igor Smolnikov's deflected cross to loop into the top corner and rescue a point for the hosts.
Yet Diego Simeone's side remain unbeaten in Group G and Gabi was content with Atletico's display.
"We have again shown that whoever plays can do well," said the midfielder following the stalemate.
"The team has done everything possible to take the match. We are in a very good position and we want to continue."
Atletico are top of Group G with 13 points from five matches, while Zenit's qualification fate will be decided in the final group games.
