It was a firm header from the centre-back midway through the first half that meant the Reds were leading 1-0 at the interval of the tie at the Bank of America Stadium in Charlotte.
However, Dortmund struck back after the break with Christian Pulisic winning and then converting a penalty before grabbing a second goal shortly after.
The Bundesliga club made certain of the victory when Jacob Bruun Larsen swept in a third in the 92nd minute.
Asked whether his overall emotion at the end of the game was frustration, Van Dijk told Liverpoolfc.com: “Yes, I think so. There are a lot of things we need to improve but it’s pre-season and we have worked hard to improve other aspects of our game, so it’s bit of a pity that we lose in the last five minutes of the game.
“We still have things to improve on and that’s what we are working on every day.
“It was very humid today, hot, and I think everyone had to dig in. We have trained a lot over the last couple of days, this morning as well, but it’s all part of the pre-season; getting fit and getting better, basically with the hard work we have put in.
“And you want to play today's kind of games and get ready for what’s coming this season.”
Van Dijk’s goal was only his second for Liverpool – with his maiden strike coming on his debut for the club against Everton at Anfield back in January.
He admits he’s hoping to add to his competitive tally during the course of 2018-19, adding: "It’s been a while but it was a great corner from the boys. Robbo [Andy Robertson] put in a great delivery and I’m happy I could score the goal.”
Van Dijk and his teammates have been cheered on by thousands of Liverpool supporters since arriving in Charlotte on Saturday morning.
They showed their appreciation for that backing as they thanked fans inside the stadium after the final whistle.
Van Dijk said: “I’m very proud to play for this club and you see the turnout, it’s fantastic and I’m enjoying every bit of it and hopefully it’s going to be the same in the next few days.”