If I don't ask for a recommendation letter from a postdoc I did research with, will it look bad?
Admissions committees expect letters to be signed by professors.  It is perfectly normal to get a letter from the professor who supervised the postdoc.  The only case where I would expect the postdoc to even be mentioned in your application would be if you published a paper with the postdoc which did not include a contribution from a professor.

Keep in mind that professors often ask postdocs to help them write letters of recommendation.