A free-kick from Matt Grimes put the Grecians ahead and although the hosts had midfielder Sam Morsy sent-off, a Eoin Doyle penalty earned them a point 12 minutes from time.
The result saw the Spireites leapfrog Rochdale into second place and remain just two points behind League Two leaders Scunthorpe.
"We were honest, we huffed and puffed and chopped and changed but it wasn't a great day for us in terms of penetration and quality and that's disappointing," said Cook.
"But at this stage of the season, all you can do is keep going and it's so important that we've moved up to second with three games to go. There are five teams now in the race for three places and we are one of them. What we need to do now is get promotion and get over the line.
"Last week we were on a high, now we are a little bit flat and next week might be different again. We have a fantastic game at Dagenham on Monday, it's a big game for us as a club and a win there would put us in a very strong position.
"I think it's a great point for us today, it's a point nearer where we want to be and we've moved up a place in the league."