Police made 180 arrests, of which 163 were from Gelsenkirchen and 17 from Dortmund, in what appeared to be planned violence on the streets of Dortmund hours before the game, which Schalke won 2-1.
The local police authorities said it had been a quiet night with the clashes occurring only prior to kick-off.
They were successfully able to segregate the two groups of fans as they left the Westfalenstadion after the game, but Heldt said the behaviour of several hundred hooligans had been a major letdown.
Both clubs sent appeals to their sets of fans not to cause trouble, but those were clearly ignored.
"This is not what we expect," Heldt told reporters inside the stadium.
"Both clubs released a statement before the game and we would have hoped that the rivalry was consigned to the pitch.
"It is not nice and unacceptable. Maybe we will eventually manage to restrict emotions to the chants and singing."
Police had expected trouble and had quadrupled their efforts in a bid to ensure a peaceful afternoon.
However, according to a police statement, groups of rival fans had chosen different routes to the ground to catch them out, resulting in clashes which the police struggled to separate with tear gas and water cannons.
"We had to take tough action to overwhelm the hooligans," said a police statement.
"It is a shame because this has got nothing to do with fan culture."
Several incidents in and around stadia in Germany last season led to proposals for new tough rules to be introduced.
The German Football League (DFL) categorically ruled out scrapping standing terraces and, apart from a few flares, there was no real trouble inside the ground.
Instead, violence is taking place outside the grounds, and some of it appears to be organised too.
Last season, a bus full of Cologne hooligans forced a bus carrying fans of their rivals Borussia Monchengladbach to pull over in a motorway service station before launching bricks through the windows.
Given that the bricks were painted in the colours of Cologne, and that a similar incident occurred weeks later, the attack was clearly premeditated, like much of Saturday's violence - the worst at a Revier derby in years.
"The Dortmund and Schalke hooligans were aware of our security measures and tried to undermine it," continued the police statement.
"Contrary to the announcements, they arrived in secret. The aim of this was quite clearly to look for violent clashes with people who were not involved and with the opponents."
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