Will Grigg gave the Spireites the lead in the first-half but they conceded twice in three second-half minutes at Roots Hall. It means their 15-match unbeaten run comes to an end but they remain top by five points.
“Sick, disappointed, sick,” Cook said at full-time.
"We got to a stage in the game where I felt we were okay, without playing well, we never played well today, we never got going. We never had any type of dominance or security in the game.
"To give the two goals away is not nice. They are just two absolutely bad goals. Rather than get into my own stuff I would much rather compliment Southend. It was a great atmosphere in the stadium.
"We have had loads of plaudits lately, we have had national media and everything, so today is Kevin’s day with his players and supporters and we wish them well.
There was little action early in the second-half until Branden Horton gave a penalty away and then a deflected second goal turned the scoreline around.
Cook continued: "Our lads have earnt one or two of these days. We have got to accept that. Does it make it right? No. But unfortunately it has not happened to us. I don’t want to whinge. The referee didn’t cost us the game.
"We should have gone on and scored the second and third goal but we were just giving the ball away all the time and then the two goals are what they are,
"There was nothing in the game, for both teams. It was a bit like to Altrincham in the second-half where you are watching going ‘urgh’ so today we lick our wounds. But I certainly want to play Southend a massive compliment to say well done.”
He added: "At the end of the season we will have a points tally and I pray to god it will be enough to get us over the line. Only time will tell. We are going to lose football games, we are not some invincible team. They have been on an amzing run and the lads deserve a massive pat on the back. We have not got ahead of ourselves at any point. “