It certainly was, but it was also not particularly important either. Losing the support of his party was an inconvenience of course, because it made things just a little harder for him, but ultimately the party banner that anybody of his political seniority runs under shouldn't matter a great deal.
I would've respected Joe if he had just chosen to run as an independent from the beginning, but he didn't. He wanted to have it both ways. He loses the primary, and still finds a way to get on the ballot in the general. Only a true egomaniac would do that.
And it's also infuriating that Lieberman blatantly lied throughout the duration of his general election campaign.