The Quakers needed to win by a large margin to stand any chance of finishing seventh. But the home side appeared to be heading for defeat after Danny Williams' strike in the first half.
However, after a scramble in the box from Neil Wainwright's corner, Cooke bundled the ball home with his head.
But, the strike was to prove too little, too late for David Hodgson's men.
The Quakers boss rued the lack of firepower behind his side's failure to secure a play-off spot.
He said: "I wanted us to leave fans with a nice taste in their mouths after today. We ouldn't really rise to the game, and I thought a lot of our decisions were bizarre.
"I'm angry with today's performance, but on the whole this season I am proud of what we've achieved.
"We've come quite far without a strike force. We lost three forwards who would have guaranteed us at least six or seven goals between them."
Denis Smith was disappointed his Wrexham side couldn't end on a winning note.
He said: "We shouldn't have had to settle for a point because we had enough chances to kill them off. I was very pleased with our shape and the way we performed.
"It would have been nice to have won and reach over 60 points. But it's been our inability to keep clean sheets and kill teams off."
On the hour mark, Williams' 20-yard strike gave Quakers keeper Sam Russell no chance.
From then on both sides were wasteful in front of goal. As Quakers looked for a quick reply, Carlos Logan found space on the edge of the box but the winger sliced his shot wide.
Akpo Sodje should have done better after taking the ball past Andy Holt, but he pulled his shot wide.
Williams failed to add to his tally when he wildly blazed his shot high over the bar.
The woodwork then came to Wrexham's aid twice in a minute. First, Logan's free-kick curled round the wall and off the upright with keeper Michael Ingham stranded. Then Ingham produced a superb save to tip Guy Bates' drive on to the bar and over.
But, just as Wrexham appeared to be heading for only their fourth away win of the season, Cooke was able to direct his header past Michael Ingham after a melee in the box.