The Spireites secured seventh spot after a goalless draw against Woking in front of more than 9,000 at the Technique Stadium.
The Blues will travel to Halifax a week on Tuesday in the play-off elimination round.
Town would have missed out on the play-offs had they lost because Dagenham and Redbridge beat Wrexham.
"We probably got in the play-offs like I thought we might and knew we would,” Cook told the DT.
"At times it was very painful, stuttering, not playing particularly well, but we are in the play-offs.
"At the minute we know we are not the best team in the play-offs, but there is no reason why we can’t win the play-offs.
"We have got to keep working at it, my big thing is repetition and believing in what you do.
"We are not playing well, it is there for everyone to see.
"But the point is we have got in the play-offs and that is an achievement."
On playing Halifax, Cook added: "They are a great team, good club, good manager, good players, very well versed in how they play, very solid, got good players at the top end of the pitch so we are going to have a tough night but we have got to make sure Halfax have a tough night as well.
"Our players are trying their best and we go to Halifax now in the play-offs and it will be a big night for us and hopefully it can be a good night because one thing we know is that our supporters will turn up and we have got to make sure as a team we do our best to turn up.
"Anything can happen now, we travel to Halifax in a really good game, it will be a great night."
Cook scrapped three at the back for a four-man defence and he says they will generally stick with that now.
He explained: We lack width, we lack penetration, we have not got many crosses of the ball, so you can write books on what we lack sometimes.
"We have gone back to the formation that I enjoy, that is the formation that I will play going forward, I will flitter with formations now and again but in that I think you have got everything – solidity, flair players on the pitch.
"We have got to be based off a lot more honesty and work ethic at the minute, we are not going to evolve into some mad team that is going to play open, expansive football, we are nowhere near those levels.
"We are a team that stutters, at times we look like we might get into a bit of a rhythm and then we do some silly stuff. But the players are not dishonest, the players are actually trying their best.
"We have been conceding goals and not scoring goals but today I felt we looked a lot more solid without the ball. When you are struggling for something on a pitch you have got to be built of something and for me the most important thing was to be built off a solid base.
"The game probably had very few chances in it for both teams, no different to the Stockport game. And those games are normally decided on a margin and normally when you have got flair players and goalscorers they are the ones who step up to the plate and at the minute we are struggling with those types of people who step up and win us the games. So we are going to be based on solidity and hopefully we can see where that takes us.”
On the performance overall, Cook, who said Akwasi Asante and Joe Quigley missed out due to injury, added: "When they put four minutes (added) up all you can think about is ‘please god don’t these score’ because our fans would have gone home so unhappy snd so flat and that would have led into the summer.
"The biggest bonus today was the crowd, our supporters are solid, they crave to deliver that success that they have seen at this stadium before. As a manager today it made me so proud to see that unwavered support for the team, it was fantastic.”