The 27-year-old rued his side's inability to preserve their lead, but insisted that the team can be content with a point against the reigning German champions
Toni Kroos had put the hosts ahead in the anticipated clash at the Allianz Arena, before Mario Gotze levelled for the champions just seven minutes later as the points were shared.
The result leaves Bayern eight points clear at the top of the Bundesliga, and 11 ahead of Jurgen Klopp's men though Gomez is nevertheless reticent about the draw.
"These are mixed feelings. At the end you have to win the game. We had three huge chances," the Germany international told reporters after the game.
"It's a draw. We can live with that. But at such a stage, you want to win, of course. Then you sit in the dressing room and look at yourself. We don't know whether we should be angry, or should simply [be content]. I don't know."
Meanwhile, Dortmund goalkeeper Roman Weidenfeller was more satisfied with the result at the Allianz Arena.
"We can be happy with the point. We need to get the points in the next games. The championship has not been decided today," the 32-year-old is quoted as saying.
"We have shown we can compete. Bayern have a great squad, but we also have a great team."
Both sides are in Champions League action on Tuesday, as Dortmund host Manchester City and Bayern welcome BATE Borisov.