The Super Eagles were eliminated by hosts Morocco on Wednesday night, losing on penalties after extra time ended goalless.
Osimhen noted that reaching the last four at two successive AFCON tournaments was no small achievement, stressing that the team’s consistency at the highest level of African football should not be overlooked.
"I have to say I'm extremely proud of this squad – the previous one and also this one – because it shows that we are one of the best footballing nations in Africa," said Osimhen.
"It's disappointing not to get to the final – we wanted it really bad because we've been working so hard from the disappointment of not reaching the World Cup, and now this.
"I think, of course, we just have to keep it moving and I think there is more and greater things to come from this squad."
Nigeria’s potent front three of Osimhen, Ademola Lookman and Akor Adams failed to launch against Morocco and their leading man says it speaks to the difficulty of the fixture on the night.
"They are also good tactically, and I think nothing clicked for them either – they got their moments too, just like we had our moments, but their defence and ours were always alert," he defended.
"Their strikers didn't get any ball or didn't play that much, and we also struggled to pass through them, but when you play with this kind of team, you expect it to be very tough.
"So, for me, I think it's not about the forwards being up there [getting the job done] but for us to get to the penalties, that's why I say, football happens and it's a game of luck, so we just have to keep it moving."