Liverpool's Van Dijk frustrated to draw Everton's 'cup final'
James Tarkowski struck a stunning equaliser deep into stoppage time to spark jubilant scenes among the Toffees' support, some of whom spilled onto the pitch.
Everton's Abdoulaye Doucoure then sparked a melee by celebrating in front of the Liverpool fans at full-time.
Doucoure and Liverpool midfielder Curtis Jones were sent-off before the Reds' manager Arne Slot and his assistant Sipke Hulshoff were also shown red cards for their protests towards referee Michael Oliver.
A draw edges Liverpool seven points clear at the top of the Premier League, while Everton move 10 points above the relegation zone in 15th.
"It was always going to be intense," said Van Dijk.
"Very disappointing to concede in the last second of the game, or even over extra time, but it is what it is. It isn't easy to accept it, especially in the manner how, but we take it and move on.
"I think the referee had a big part in the game today in terms of certain challenges were given as fouls and similar weren't. In the end it is just disappointing to concede a very good strike, but a disappointing one.
"This is their cup final and they would try to do everything in their power to make it difficult for us. It is a big boost for them but a blow for us."
Everton are set to move to a new 53,000 capacity stadium next season and Goodison was given a fiery goodbye in the last clash between the two sides, whose stadiums are separated by less than a mile.
"It was mayhem all game," said Everton boss David Moyes. "It was an old fashioned throw back in some ways.
"I think it was hugely important that Evertonians get to finish as best they can in this stadium.
"Overall the support in here was unbelievable tonight. Incredible support and it was fitting they got the ending that they did."
Everton fans have grown tired of living in Liverpool's shadow in recent decades.
They were reminded of a 30-year drought without a trophy by 30 balloons among the visiting support.
Moyes returned for his second spell in charge last month and said restoring the nine-time English champions to their former glories is his goal.
"We want to get back to being a big club again," added the former Manchester United boss.
"We've got a long way to go, we've got a job to do first of all this year to be a Premier League club and then kick on."