The F1 team dismissed Horner after 20 years as team principal earlier this month and the motorsport advisor explained that the lack of performance on track this season was just one of the reasons behind his departure.
Marko told Sky Germany: "The decision was made by the management - that is, Oliver Mintzlaff.
"We informed Christian Horner of it in London. At the same time, we officially thanked him for 20 years and eight world titles.
"It was the result of various factors. But primarily, performance was not quite where it should be."
Horner has been replaced at Red Bull by Laurent Mekies - who has been promoted from running junior team Racing Bulls - and Marko believes that the Frenchman's engineering background can help the team in an increasingly technological sport.
He said: "Luckily, we were able to bring in Laurent Mekies from within the Red Bull family. His role will be significantly more focused - primarily on racing.
"He's an excellent engineer, which is a good fit considering the complex technology in Formula 1.
"We've already seen that he communicates very well with the staff. We're hopeful that we can gradually return to the top."
Marko believes that Mekies' technical expertise will prove beneficial as Red Bull follow other teams who have put those with engineering skills in charge.
The Austrian said: "I believe that's definitely an advantage. Other teams have gone this route before us.
"Also, the scope of the role has been clearly reduced. The company has 2,000 employees. Mekies will mainly focus on the technical side and racing.
"Marketing, the RB17 project, or Powertrains are each handled by separate departments. So, he can dedicate his full energy to racing success."