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The Reds slipped to their first defeat at Anfield in over a year on Tuesday evening, losing 1-0 to the reigning Serie A champions.
Liverpool have still qualified for the quarter-finals of the Champions League 2-1 on aggregate, but talkSPORT's Adrian Durham believes van Dijk made a costly mistake for Martinez's strike.
He asked: "What are Liverpool doing for the goal? Joel Matip gives it away needlessly. And watch Virgil van Dijk…
"World’s best defender? Just dangling a leg and letting Martinez shoot?
"Does he not realise how good Martinez is? He got a hat-trick at the weekend!
"Unbelievably bad defending from Van Dijk. It’s not often you get to say that."
Alexis Sanchez played a pass to Martinez, who let the ball run for a few seconds before unleashing a stunner with his right foot.
Van Dijk often looks calm and composed at the back, but he's been criticised in the past for looking lazy in his approach.
Martinez's strike got Inter back in the tie but moments later, Sanchez was sent off for a second bookable offence.
The Chile international received his marching orders after a tackle on Fabinho and it swung momentum back in the home side's favour.
Mohamed Salah hit the bar twice while Luis Diaz was denied by a remarkable Arturo Vidal block.
Liverpool are still on course to win a historic quadruple after winning the Carabao Cup late last month.
Jurgen Klopp's side are in the FA Cup quarter-finals and sit six points behind Premier League leaders Manchester City with a game in hand.
"I’m glad we don’t face Inter every week, they’re a very tricky opponent," Klopp told BT Sport in his post-match interview.
"They are fighters, they are warriors. "The difficulties we had were pretty close to what I expected. Inter are a really, really good side, set up for these kind of games.
"Without playing brilliantly we had clear-cut chances. Over the two legs it's completely fine that they won one and we went through. We could've done better against an opponent that makes life uncomfortable.
"It was a really interesting game. In the end we lost the game which obviously is not cool, we didn't come here to lose a home game."
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