It was a disappointing way to mark Preston's 5000th league game, as Wayne Rooney's free kick proved to be the difference.
Going into the game, Cocu knew his side would be in for a tough tie and wanted to knock the belief out of PNE during the encounter.
He said: "We all knew it would be a difficult game. We were on an equal amount of points and were level in the league.
"They really pushed us to our maximum. It was a good goal by Wayne but I was disappointed we couldn't score the second one.
"My thoughts were that if we could score the second one they wouldn't believe any more,in a good result.
"It stayed an open game until the last second of the game where the goalkeeper almost scored the equaliser.
"We showed good character in the end when we needed it to defend well."
Being in cotnrol of the ball, as Derby were in the opening 45 minutes was exactly the gameplan the Dutchman arrived with.
The Rams limited North End to few clear chances throughout the game.
"We knew that they really needed a good result today because they haven't had a win in quite a few games," Cocu said.
"We knew that if we could control the game and be dominant on the ball that we could get the space that we needed to be creative in the final third.
"Some stages of the game we did very well and we did it but to be fair they played a game and they pushed us back in some stages a swell.
"It was a tight game but in the end it was a good game for us. .