When Kirk said he would die alone, the implication was that when his time came, his friends/surrogate family would no longer be with him, meaning Spock/McCoy primarily.
When he was saved from "God", he said to Spock "I thought I was going to die", to which Spock responded "Not possible, you were never alone" implying that because he (Spock) and the crew of the Enterprise were there, they would fight to give him a chance to survive and succeeded once more.
In Generations, Kirk didn't die on the Enterprise B, he died on a desolate rock, in an idiotic manner, with no one close to him anywhere nearby to comfort him in his last moments, except for a stranger who claimed to be the Captain of another Enterprise that didn't really mean anything to him. So Kirk, did in indeed die forgotten, and alone as he suspected would happen.
