The Merseyside derby was the last played at Goodison Park before Everton's move to their new stadium.
The match was a typical thriller, with James Tarkowski hitting an injury-time equaliser. Abdoulaye Doucoure, Liverpool midfielder Curtis Jones and manager Arne Slot were all sent off at fulltime.
Van Dijk later said, "Intense, it was always going to be intense. A lot of battles. 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."
On the title race, he added: "We have a lot of games up until the international break. We have put ourselves in a very good position and that is down to hard work, quality and consistency. We just have to look at ourselves, don't look at what others do, just try to focus on ourselves and be the best version of ourselves.
"We have put ourselves in a good position, let's keep going."