Fans were told before the game that away fans would be held inside the stadium for at least ten minutes after the full time whistle.
However, many fans have reported on Twitter that the Sheffield United fans were released at the same time as the home fans, leading to clashes around Leppings Lane.
Fans reported fireworks and coins being thrown as supporters left the stadium with one fan taken to First Aid after being hit by a firework.
Others reported crushes between sets of fans on Leppings Lane with sets of Sheffield United and Sheffiield Wednesday fans on the same trams.
One fan tweeted: “All kicked off outside away end, they let both sets of fans come out together with no segregation.”
Another tweeted: “What an absolute shambles from @syptweet. It was like a warzone outside Leppings Lane. Had to squeeze through the coaches to stop from getting pelted with coins, smacked by a moron, or trampled by horses. Easier to police on a Monday night? Yeah right! #swfc #twitterblades”
An earlier video showed a fight breaking out outside Hillsborough with police officers quickly breaking it up.
South Yorkshire Police said there was ‘disorder’ when the two teams came into contact at the tram stop at Leppings Lane.
However, the force said this was ‘effectively dealt with by officers’ and that no issues were raised by tram operators.