Cody McDonald's second half header was enough to secure the points and keep Gillingham at the top of npower League Two.
"It's a fantastic performance all-round from the squad," Allen said. "The great thing is there are so many players who can go in and play.
"We defend as a team and we attack as a team. We played one or two touch football, moved the ball about and though it was a bit scary in the last 20 minutes, we've seen it a million times. When we defend in numbers we are strong and we are not left open.
"It's a victory for the club and it's an historical day to be honest for the club, the players, supporters, chairman and to be manager and get this record makes me very proud.
"Breaking a record of 100 years is fantastic. Deon Burton came in at the end and said 'well done lads, we've made history' and that's all we spoke about. To be the squad and part of the club when we made history is quite amazing."
Chesterfield boss Paul Cook knows the chances of staging a promotion challenge are fading after his side became the latest to be frustrated by Gillingham.
He said: "We huffed and puffed and we did okay and certainly in the second half I thought we could have gone on and win the game but unfortunately for us it just didn't happen.
"I can't fault the effort or application and we created two or three chances but it's obvious that we are not scoring enough goals. I thought we did our best and we knew it was going to be difficult because of the way Gillingham set up but we lacked a bit of quality.
"While it's physically possible we will move heaven and earth to do our best but it looks to be too much of an ask at the minute but as a manager you have to keep believing."
- Sports & Recreation