The Federation didn't do nothing; they condemned the Klingon attack.
The Federation Council only decided to condemn the invasion once it had happened and was public knowledge. Before, when they knew that the invasion was coming, they ordered Sisko and the others not to warn the Cardassians.
Even if what the DS9 crew did in warning the Cardassians through Garak had lead to a full-scale war with the Klingons, how does that negate the fact that it was the right thing to do? You don't sit back and let a massacre happen if you can stop it somehow if you're a moral person. And saying that the Federation Council only ordered them to be quite while they pursued communications with Gowron and the High Council doesn't matter either - they were still willing to let the invasion happen.