The winger scored twice in the Reds' 3-2 win over Norwich City, which moved them five points clear in the Premier League title race.
The visitors moved five points clear at the summit of the Premier League table with the victory, which was their 11th win in a row and takes them closer to a first title in 24 years.
Sterling, 19, scored a stunning opener from 25 yards in the fourth minute and added the third in the 62nd with a deflected strike, while the England international also set up Luis Suarez's 30th league goal of the campaign in between.
"We have tried to play him in different positions to improve his football intelligence. He started at the tip of the diamond today and moved to the right side of a front three. He's a really humble kid and he's got that in-built brain and belief."
Liverpool was boosted by Chelsea's shock home defeat to Sunderland on Saturday and will be guaranteed the title if it takes seven points from its remaining matches against the Blues, Crystal Palace and Newcastle.
Asked about the pressure of the title challenge, Rodgers replied: "I enjoy it. It's brilliant. I've worked for a long time as a young coach. By the time I arrived in management, I'd been an apprentice for 15 years. My aim as a coach is to make players better and the consequence of that will be winning.
"To live with expectancy is all part of being at a huge club like Liverpool and it's something I'm very privileged to do. I know the players are giving me everything — it's 11 wins on the spin now and that's an incredible achievement."