Van Dijk was one of two Dutch players to miss in the shootout after an ill-tempered quarter-final ended 2-2.
The Dutchman said his focus now is on guiding sixth-placed Liverpool back into the Premier League top four, though a title challenge looks unlikely as they sit 15 points behind leaders Arsenal.
“It has … motivated me here (at Liverpool). We are quite some points behind Arsenal but the season could be a very crazy one, a very strange one,” he added.
“We have to be realistic and we’re not thinking about the title at the moment. We have to focus on the game ahead of us, win games, and then we’ll see.”
The World Cup quarter-final against Argentina had 16 yellow cards and one sending off, with Van Dijk involved in an altercation with Leandro Paredes where he shoved the midfielder to the ground.
Van Dijk said he has since had some time to reflect on the “intense game” and hoped to lead the Netherlands to Nations League glory at the end of the season on home soil.
“(The shove on Paredes) was obviously something I don’t normally do but it was the heat of the moment and we are all human beings, these things happen,” Van Dijk said.
“It fuels me in any way, shape or form because I want to be successful with the Netherlands. I feel like we have a fantastic squad and new era with Ronald Koeman coming back (replacing coach Louis van Gaal) and young players coming through.
“Hopefully we can do something nice in the summer with the Nations League finals. That will be a nice step and it is something I really want to win, even though it’s the end of the season when you are probably absolutely shattered.”