At the end of Balance of Terror Kirk mourns with a junior female officer at the loss of her fiance, a junior weapons officer. Kirk had been in the process of marrying them when the episode began. I understand that this is an exception to the red-shirt rule, in which Kirk willl deliver a few testy lines "a member of my crew is dead!" before moving on, but it's worth noting in context of Picard 'thank you very much, moving on' attitude at the end of Generations.
Except Picard does morn Kirk. Deeply. It's one of the few good shots of the film.
There was no reason for him to mention the Nexus or Kirk or any of that. Kirk was best left remembered as the guy who died saving the successor to his legacy.
Are you referring to the scenes in which Picard watches Kirk die and then buries him beneath a cairn? I can somewhat accept that, but still feel Kirk deserved more. Maybe a service of some sort with the captains of the three Federation vessels, which came to rescue the E-D crew?