The abrasive Matthaeus heavily marked Maradona in the 1986 final in Mexico City, yet the diminutive Argentinian, who died from a heart attack on Wednesday at the age of 60, still inspired his side with a stunning display in a 3-2 victory.
It was Maradona's superb pass which allowed Jorge Burruchaga to score the winning goal four minutes from time at Estadio Azteca.
The defeat was avenged four years later when Matthaeus captained West Germany to a 1-0 win at Rome's Olympic Stadium in the final of Italy 1990.
Games against Maradona "were big, exciting duels," Matthaeus, 59, told German daily Bild.
"These are moments that I will always have in my heart.
"It was always a challenge to stand up to him. He's been with me for half my life -- he was my best opponent.
"He passed away too early at 60. The news makes me very sad."
The German says Maradona had a talent matched only by Argentina's current superstar Lionel Messi.
"The ball always obeyed him, even at the highest speeds, as you might only see with Messi today," Matthaeus said of Maradona.
"The best thing you could do was not let him get the ball."
The German says mutual respect led to an unusual friendship.
"He had a big heart, was generous. You felt like he was always there for you," Matthaeus added.
"It wasn't a normal friendship. Our relationship was characterised by the greatest respect for one another."
Matthaeus said Maradona's death was a "shock, even if you were a little prepared for it due to his lifestyle.
"We last saw each other at the 2018 World Cup in Russia.
"The impression he made wasn't the best back then, but no matter how he lived, what matters is his legacy and what he has done for football."
Although Matthaeus rates Pele as the world's best footballer, because the Brazil legend won the World Cup three times -- twice more than Maradona -- the Argentine is "right behind him."
"He was one of the greatest in football."