Goals from Jake Wright jnr and Danny Elliott saw Boston leapfrog Kettering Town to finish seventh in the National League North.
They now travel to Kidderminster Harriers for Thursday's eliminator.
Boston faced a nervy wait after their 2-0 win at Farsley Celtic as Kettering, who leveled in stoppage time, were five minutes behind.
"It's not over until the whistle blows, but when that happened the emotions were unbelievable," Cox said.
"We don't want it to end now, we want the fairytale to carry on now.
"We don't want to go to Kiddy to make the numbers up.
"We'll give the lads a couple of days off and plan for Thursday. It's the play-offs - anything can happen."
The Pilgrims players returned to the pitch to celebrate with fans as news of Kettering's draw filtered through.
"The support we get home and away is unbelievable," Cox added.
"We got the players out and jumping around with the supporters to feel what it means to the football club.
"The support has been absolutely fantastic. We enjoyed it, it's what we're in the game for and the boys have been great today."
Despite defeat, hosts Farsley also secured their safety after Guiseley were beaten by Alfreton.
"I'll have the beers on the bus, they deserve it," Cox added.
"The home dressing room had loads going in and I was a little bit envious."
MORE PILGRIMS: United secure play-off spot after Farsley win - report