United led 2-0 after just six minutes but goals from Ryan Colclough, Jamie Grimes and a 95th minute winner from Tom Naylor turned the scoreline around in what a dramatic clash in front of more than 8,000 fans.
"I thought on the day they were the better team,” Askey admitted.
"Chesterfield have been in this league a while now and spent a lot of money trying to get out. The standard that they showed today shows where we have got to try and be.
“We got off to a great start with the two goals.
"We were always under pressure, even with the two goals.
"It is one of those games, we have got to learn from it.
"It was tough today, we gave ourselves a great chance and then to concede right at the end, having put so much energy in, is obviously a bit of a blow.
"We had one or two setbacks with injuries that did not help.
"I have just said to the players in there that leagues won’t be won and lost with games like today.”
He added: “On the ball, we needed to be a lot more assured but weren’t today.
"We let the atmosphere get to us today a little bit, but there were still some really good performances.”