Even though it was a minority, the songs do not reflect well on the fans of either club.
Unpleasant side of football shown at Elland Road
Leeds United's Elland Road was the most hateful atmosphere that I ever played in. But all the bile and hatred, the spitting and songs about the Munich air disaster didn't unnerve me.
The Munich stuff was sad, pathetic and disrespectful to the families of those who lost their lives, but I used the other venom to motivate me.
I had always wanted to play at Elland Road after witnessing the brilliant atmosphere there against Glasgow Rangers in the 1992 European Cup.
I remember thinking, "That's what a big European game is about". I wanted to be part of that. I admired the Leeds fans for their passion and the noise they created.
Years later, I was part of that atmosphere with Manchester United - although safety concerns usually meant that games kicked off early, not long after fans had got out of bed.
You cannot beat the atmosphere of a night game under the glare of floodlights, but even those morning matches at Elland Road were not for the faint hearted.
Our team coach would park right by the entrance and we all knew what was coming next. The Leeds fans would crowd around it and shower us with abuse.
The hatred was unbelievable and much worse than at bigger rival clubs like Liverpool.
You would see kids standing with their grandfathers who were foaming at the mouth just because the Manchester United team had turned up.
Leeds loathed United and held grudges against players long after they had left for Manchester. Gordon McQueen still gets abuse when he goes back to Elland Road - and he left there for Old Trafford 33 years ago.
The atmosphere was even worse inside the ground, but it just revved me up and my response to abusive fans was to celebrate putting the ball into their net.
In April 2000, United were going for the title. So were a very good Leeds side with players like Harry Kewell and Jonathan Woodgate, captained by the South African defender Lucas Radebe.
It was a tough game and 0-0 when Radebe and I chased a ball from the halfway line. I beat him for speed and knocked him off balance, before flipping the ball over Nigel Martyn, the Leeds goalkeeper.
Get in! It was the only goal of the game and in front of their Kop end where their most vocal fans were.
The goal virtually gave us the title - Leeds would finish third which shows how far they would later fall - and I deliberately celebrated in front of the Leeds fans and watched as they fumed.
They wanted to get on the pitch and at me. I just laughed at them. They had given me abuse all game and they could not take a little celebration back.
At that moment I found it nice to be hated. Hated, but rated. I'm sure Ryan Giggs felt the same on Tuesday night when he cupped his ears to the same stand and the same fans after scoring a brilliant goal in United's 3-0 Carling Cup victory.
Radebe has reminded me of that goal many times since. He is someone I have a lot of respect for, unlike the football fans who sing songs about the Munich air disaster, or the Leeds fans who were killed in Istanbul a few months after that goal that I scored.
There were plenty of both at Elland Road the other night. It is not like they meet in the league these days since Leeds have long since been relegated from the Premier League.
And even though it was a minority, the songs do not reflect well on the fans of either club.
A lot of it is bravado in front of their mates.
Fans spend the week working in tough jobs and then go to the match thinking they can say what they want from the safety of the crowd.
They want to vent their frustrations on football players because they think that makes them more of a man.
They think they are anonymous and can shout what they want, even if it is mocking people who have died.
It is similar on the internet. I have seen footballers try to communicate with fans - something they are often accused of not doing enough - through Twitter. What do they get in return? Loads of abuse from anonymous haters. Faceless in a crowd, faceless behind a computer or a mobile phone, it's the same thing. Why should players even bother? There are better things to do.
The vile songs and abuse will continue because some fans like to provoke a reaction, even at the expense of a loss of life.
That is where the buzz is to them, those sad little individuals who thrive on hate.
Andrew Cole's column is written with the assistance of European football correspondent Andy Mitten.