The Manchester United loanee was handed his debut in the 2-0 home defeat to Millwall, coming off the bench as a 55th-minute substitute.
Berg is confident King can make a valuable contribution to the Rovers side, starting with the Lancashire derby against Bolton on Wednesday.
King’s manager told the club’s official website: “I thought he did okay. Obviously it will take a little bit of time before he gets used to everything.
“But he showed in parts of his game that he can give us that little bit extra with his offensive runs in behind, he can take people on and get into scoring positions.
“We want to play a game as quick as possible so it is good that on Wednesday we have Bolton. We know we can play better than we did against Millwall and that is what we intend to do on Wednesday.”
Rangers centre-back Russell Martin will miss Scotland's friendlies against Costa Rica and Hungary through injury.
Jonathan Walters is ready to continue his Republic of Ireland career when he returns to full fitness, according to Martin O'Neill.