Well, I think the Narn were still plenty strong compared to the LoNAW. Sure, they couldn't have taken on the other major races, but once the Centauri started making gains no smaller race interviened... I'm guessing cause the Narn were still pretty tough.
But it could also be political. After all, the Narn gave the EA several weapons to fight the Minbari, and considering Earth probably couldn't have totally afforded them (there currency was "devalued on the intersteller market"), EA probably repaid the Narn's with a seat on the council.
But most importantly, when Babyon 5 was first built and the council was set up, the Narn were still a powerful foe. I mean, the show started with the Narn's lashing out at Ragesh 3, so in the end, I'm guessing the Narn were still a pretty powerful force in the galaxy.
As for the Drazi, I remember reading that they were the most powerful military force in the LaNAW, and the show backed that up pretty well. But looking at other "on-screen" evidence, I'm guessing they have poor infustructure and diplomatic capabilities, which would limit their ability to garner intersteller recognition.
Just my 2 cents...
"We had all the momentum; we were riding the crest of a high and beautiful wave..."
- Hunter S. Thompson