The Anfield boss says the 18-year-old has a 'natural eye for a goal' after he scored the equaliser in the Northern Irishman's first game in charge, a 1-1 draw against Toronto FC
The 18-year-old netted in the 69th minute after Quincy Amarikwa had given the Canadians the lead in the pre-season friendly.
Morgan had only arrived in Canada on the morning of the match and headed straight to the bench to hug his new boss after converting from close range.
Rodgers told Liverpool's official website: "He's a really, really good kid. He's come in, he's taken everything on board that I've talked about.
"He's technically good, he's got a natural eye for a goal - if he doesn't arrive at that moment, the goal doesn't go in because the defender would have got to the line to defend it.
"He's got that natural instinct to score but I was also pleased with the cleverness in his pressing. He pressed the ball really well. That forced them into some mistakes.
"It was a great moment for him. His father flew in this morning from Liverpool, so to get here and to see the goal would have been a special moment."The former Swansea manager was pleased that his tactical instructions were followed by the players as he tries to get the Reds playing his possession-orientated brand of football.
He added: "We've still got a long way to go. It's very important that we dictate games, we control games, we dominate games. You saw for large parts of the game we forced Toronto back.
"It's just that penetration that will get better as time goes on, because possession is no good on its own.
"Some of the movement patterns were very good and it'll get better."