The former Manchester United manager believes the Brazilian provided the necessary upgrade in a clear “weakness” before with Loris Karius.
The £67 million signing shone last season as the Reds won the Champions League and Mourinho considers the Brazil No 1 the key difference in enabling Jurgen Klopp’s side to become champions.
“I think he was the last piece of the puzzle,” Mourinho told Sky Sports.
“Two seasons ago when Liverpool were already strong, not reaching, but fighting for trophies, you could feel when they reached the final, the weakness was there (in Karius).
“That boy was not at the Liverpool level, so they went for one of the best in the world. The same they did with Virgil Van Dijk.
“No doubt that was the last piece in the puzzle.”
While Mourinho also hailed Van Dijk as the best centre-back in the Premier League.
“That (the best in the world) would be unfair to some fantastic central defenders,” Mourinho insisted.
“But in English football for sure, he has everything, it’s almost impossible to find a weakness in his game.”