Bellingham has made only two starts in all competitions since joining the team this summer for a reported £26.9 million.
The 20-year-old England international signed with Dortmund after his brother Jude joined Real Madrid.
In an interview, Kovac explained that Bellingham's limited playing time is due to the high level of competition within the team.
"Everyone wants to play more, but we only have 11 players in the starting lineup," Kovac said.
Kovac also noted that Bellingham faces additional pressure due to media attention and comparisons to his brother.
"Bellingham is a talented player with great potential, but he needs to grow into the team," Kovac said.
Kovac believes that excessive pressure and media attention can hinder Bellingham's development, saying, "I think that's not doing the boy any favors, and the boy isn't doing himself any favors."
The team's next match is against Mainz in the Bundesliga, and Kovac will continue to monitor Bellingham's performance.