The Capital men were beaten 3-2 on aggregate by Jim Duffy's Dumbarton, who retain their place in Scottish football's third tier by the skin of their teeth.
The Citizens won last night's second leg courtesy of a second-half Ouzy See header, but also had defender Liam Henderson sent off after picking up a second booking for simulation.
And Naysmith believes had the visitors kept 11 players on the park at the C&G Systems Stadium, then it would have been his side and not the Sons celebrating at full-time.
"We have come up just that wee but short and there's no getting away from that," Naysmith said. "But the players were excellent and stuck to the game-plan. We got the goal at the right time and I honestly thought we were going to go on and win it in 90 minutes.
"We turned the game completely in our favour and then we lose Liam, but you still wouldn't have known we'd gone down to ten men. We tried to be as brave as we could and go for it so I can't ask anymore of them.
"The efforts they have produced and to still be running like they were when it's your 17th game in 61 days is incredible.
"But football is about statistics and we just weren't good enough over the two games."
Naysmith did allude to the second-half performance of Monday's first leg – where they conceded all three goals – as another defining moment in the tie.
"You have to look at yourself as a manager and as a player and what went wrong," he said. "So, where we fell short was our second-half performance on Monday night. We had a poor 45 minutes and it's cost us, and that's cruel and it's blunt, but football is cruel at times.
"We'll go away now and start preparing for next season. There will be changes but I want to be talking this time next year having gone up as champions."