The 17-year-old became the club's second-youngest Premier League goalscorer behind Michael Owen with his 29th-minute strike to beat Rodgers' former club Reading.
Liverpool had more than enough chances to put the game beyond doubt, but the manager was thrilled Sterling's early-season performances were finally rewarded with a goal.
"It was a brilliant goal," said Rodgers.
"We have been asking him, Suso and the other wide players to try to break the line of defenders and he's done that.
"We've been doing a lot of work on that on the training field but all the credit goes to him because he's got to identify the moment to go in.
"It wasn't an easy chance because he is going away from goal, has a quick defender tracking him and to adjust his feet and have the technique to shoot across the keeper is wonderful.
"He's a terrific talent and he's got a good head on young shoulders."
Fellow forward Luis Suarez was also at the heart of much of Liverpool's attacking thrust, but he could not add to his tally of seven goals in his last eight matches despite having a number of chances.
"He scores a lot of chances. He's not perfect, he's not going to score every chance, but he's got a great return if you look at his stats, at his goals return at Ajax and since he's come into here," added Rodgers.
"There's no doubt he'll want to be a bit more clinical and going forward we want to get some more players around him who can take the load off him as well.
"He leads the line terrifically for us. His movement and creativity is great.
"He created opportunities for himself and he'll be disappointed he hasn't scored today [Saturday]."
Rodgers also praised goalkeeper Brad Jones, who made his first Premier League start for the club after Jose Reina was ruled out with a hamstring injury.
"I thought Brad was outstanding: what he had to do he did very well," he added.
"When I came in during the summer he had been the number three keeper but I've seen massive development and it's a great credit to him.
"What he is absolutely outstanding at is shot-stopping and he made a great save from (Gareth) McCleary."
Reading manager Brian McDermott was pleased with the way his side came back in the second half and thought they could have earned a draw.
"Liverpool never really hurt us with their passing moves but did so with one ball over the top," he said.
"In the second half we were right in the game and I honestly felt we were going to get at least a point and we were on the front foot right till the end."
Reading substitute Jason Roberts carried out his vow not to wear a 'Kick It Out' T-shirt in the warm-up in protest at his perceived lack of action in combating racism in football.
McDermott was fully supportive of the 34-year-old's actions.
"I spoke to Jason about that and he was very clear in his views. He had his reasons and I support him 100 per cent," he added.
"When you consider what happened this week with Danny Rose (who suffered racial abuse in an England Under-21 match in Serbia) hopefully we can put these issues to bed.
"I wrote to Danny actually as I thought he conducted himself really well.
"But it doesn't belong in society and it certainly doesn't belong in football.
"It is an emotive subject and rightly so. I can only speak for my players and Jason feels very strongly about this so I back him 100 per cent."