I ignored the Klingons and destroyed the Doomsday Device, the mission ended fine. You could have run into one of those "mission not completing" bugs.
"Don't let them promote you. Don't let them transfer you. Don't let them do anything that takes you off the bridge of that ship, because while you're there... you can make a difference." - James T. Kirk
What has helped me is warping out and then right back into the same sector. Most times it goes ahead and the ending text pops up. Not all the time, though. Just one more thing that needs to be worked on.