Jose, the only Fertilome I could find that mentioned quackgrass was an over-the-top product for gardens (so it is not for use on lawns). Do you have a link to a specific product? For Trimec Crabgrass, the label does not mention that it controls quackgrass and also notes the grasses one should not use it on. Is there another one you were thinking of?
Not all herbicides that kill certain grasses are safe to use on other grasses, and not all herbicides that kill grasses kill all grasses. So you really need something that specifies the grass that you want to control.
Glyphosate spot treatment is what is usually recommended for quackgrass, which is quite difficult to control. Or just fertilize and mow and eventually it will get over its spring spurt and not be noticeable.
Quackgrass control in turf from Michigan State U Extension: