Cornelius has moved to the Bluebirds from FC Copenhagen on a £7.5m deal, but Mackay has expected he might miss out on bringing the 20-year-old to the Premier League.
The 41-year-old told reporters: "Andreas has plenty of potential. We'd been watching him for a year and thought we would miss out. But we managed to get him.
"We think Andreas is a really top player. He was player of the season at Copenhagen and has scored plenty of goals.
"But he adds to the quality we already have up front and to the squad that got us to the Premier League."
The Danish international scored 20 goals in 44 appearances for Copenhagen last season.