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The Coasters beat Boston 3-0 to secure promotion to the fifth tier and have scored 105 goals in the process, breaking Chester's record.
The club have reached the play-offs in the previous two seasons but missed out on promotion.
"It's a really emotional day," Challinor told BBC Radio Lancashire.
"I don't think things will sort of sink in, but we'll enjoy next week and enjoying walking out at our home ground as champions.
"It has been a tough season with things going on away from football.
"To get over the line and to achieve what we have is a very, very special day.
"It will be a special day as it is not often you get the chance to play with a freedom and not a great deal on the game - to walk out in front of our own fans will be fantastic."
AFC Fylde manager Dave Challinor has praised his team after they won the National League North title for the first time with a game to spare.