The England international, who scored his spot-kick in the shootout after the match ended 1-1, appeared to be upset at something said after the game and climbed into the crowd.
Video footage showed Dier climbing over seats and becoming involved in a fracas before he was restrained by security guards.
It is believed his brother was in the section where the incident happened.
Premier League
Klopp: Liverpool owners FSG are 'good, reasonable people'
4 HOURS AGO
"I think Eric did what we professionals cannot do but probably every one of us would do," Tottenham manager Jose Mourinho told reporters. (Reporting by Martyn Herman, editing by Ed Osmond)
Football
Cantona: 'Fans are the most important thing in football'
4 HOURS AGO
Premier League
Premier League clubs will tell ’big six rebels’ to quit – Paper Round
3 HOURS AGO