The 26-year-old winger came off the bench in the 83rd minute at Luton on Sunday and scored a dramatic equaliser deep into added time to earn a 1-1 draw.
He lifted his shirt after his goal to show a message reading "Freedom for Papa" and after the match released an emotional statement on Instagram pleading with his father's kidnappers to release him immediately.
It was his first appearance since Luis Manuel Diaz was abducted in the northern Colombian town of Barrancas on October 28. Diaz's mother was also kidnapped but was rescued hours later.
The head of Colombia's ELN guerilla group on Saturday acknowledged the organisation had made a "mistake" when it abducted Diaz's father and vowed to work toward his release.
Following the game against Luton, Liverpool defender Van Dijk said: "He's been training with us, knowing that it's so fresh, what's going on. He feels like being with us is a safe place, so it helps him.
"We're here for him. We mentioned it last week, it's an absolutely horrible situation. Hopefully there will be a solution. We'll be here for him and everybody should support him. Hopefully it will be sorted as soon as possible."
Liverpool had looked set to fall to a shock defeat before Diaz's late intervention, trailing to an 80th-minute goal from Luton substitute Tahith Chong.
"He's still disappointed because he also wanted to win," said Van Dijk. "There's a lot of emotions in his head. It must have been (meant to be) that he should have scored. I'm happy for him, but hopefully we can get his father back as soon as possible.
"You can't imagine it, that's the scary part. The only thing we can do is hope they will find him safe and sound and they get him back to his family.
"When it happened it was a shock to everyone. We spoke about it and it should give us extra motivation. He doesn't want us to suffer from what he's going through, he wants us to take fuel from it."
