First-half goals from Scott Fenwick and Jordan Hugill secured the decisive three points as Pools, who were 10 points adrift at the foot of the table in January, secured their Football League status.
The result consigned Tranmere to a second successive relegation, with Cheltenham also going down.
“What an absolutely fantastic day,” said Moore. “It was a long day, and a long second half.
“But they gave absolutely everything. That’s what we have wanted from them and that’s the type of performance I want.
“For me as a manager, I don’t think you can better that. If you look where we were and what has happened, it’s just been astounding.
“Deep down, I didn’t think we could do it. You’ve got to say the right things and install belief in the lads.
“I have the same feeling and buzz that I had when we got back-to-back promotion (at Rotherham).
“I have said on Twitter that I think this was the biggest game in the club’s history.
“It’s not easy to come back if you go back out of the Conference. That drop would have been unbelievable. We’re a league club still and that’s fantastic.”
The day also represented a personal turnaround for Moore, who spent eight months out of the game having been sacked by Tranmere amid a betting scandal.
“I am absolutely gutted for Tranmere,” said Moore. “They are a fantastic club, and a big club. I feel for the fans there.
“I am not being big-headed but we wouldn’t have gone down last year had I been there, or this year.
“A certain person made a vital error. What goes around sometimes comes around.”
He added: “I was always thinking there wouldn’t be a phone call (to give him another job).
“It’s a betting scandal. You see on Twitter people saying, ‘He has had B#5,000 on Tranmere to get beat’ when there were actually 10 B#1 bets.
“It was wrong what happened. It was a simple mistake and I am sure the decision would have been different had we been top of the league at the time.”
Opposite number Paul Tisdale was surprisingly upbeat despite seeing Exeter’s faint play-off hopes crumble.
“We were playing against a team fighting for their lives and we knew it would be a game of mistakes,” he said. “I was hoping they would make them and not us.
“We played pretty well, but there were mistakes in the side that cost us. But all in all, I have no complaints.
“I know what we have to improve on next year. Being practical, we’ve come up short because we are short.
“But when you consider that we were bottom of the league after six or seven games at the start of the season, it’s not too bad.
“We have a chance to go forward for the first time in a while.”