The Spireites, Sky Bet League Two leaders at the beginning of Tuesday night despite coming into the game without a win in four matches, were staring down the barrel of a third straight home defeat and a fourth loss in their last five league games as they found themselves 2-0 behind with 61 minutes on the clock.
Goals from Luke O'Neill's and Ryan Jarvis had put the Minstermen in control but a Armand Gnanduillet penalty and another goal from substitute Jay O'Shea had Chesterfield level after 76 minutes.
The hosts were unable to find a winner and lost top spot in the table to Rochdale after their late home win against Northampton, but Richardson said: "People maybe have questioned the desire and you are a victim of your own success in the first quarter of the season but I don't think anyone could question the endeavour and desire (tonight).
"Teams come here now and within the last few days, two teams have line up without a recognised striker on the pitch and are looking to frustrate you with the formation. That's how teams are going to set up and we must get used to it.
"We must move the ball quicker and off the ball be a lot better and I think you could see an improvement in that. Teams come here and raise their games and we must embrace that and get used to it.
"But we will get better because we are still learning and I don't think anyone has gone away unhappy with the commitment we have shown."