Liverpool tracked Keita all summer but their transfer approaches were rebuffed by Leipzig.
However, in the final week of the transfer window, Liverpool agreed a club-record deal to sign the midfielder next summer.
The Reds paid Keita’s £48million release clause and an undisclosed premium to seal the deal a year early.
And Mintzlaff has admitted Leipzig did not expect a club to pay so much for Keita.
“We would have never given Naby Keita away if it had not been for the release clause,” Mintzlaff told German outlet Kicker.
“When we agreed on [the clause], we did not presume that only after a few months there’d be a club willing to pay significantly more.”
Keita has had a turbulent season so far for club and country.
The Guinea international was sent off against Borussia Monchengladbach for a high tackle in September.
And last week he scored but was then sent off in their 4-1 defeat to Tunisia.
But he insisted last month that his move to Liverpool will not affect him.
“For the rest of my time at Leipzig, my commitment will remain as strong as it ever was,” Keita told Sport Bild.
“Since I’ve worn the Leipzig shirt I’ve always given my all – and that will remain the case until the final whistle on my final appearance for the club.
“My future has been sorted now and I can fully concentrate on helping us achieve our objectives this season.”