Sterling opened the scoring after halftime.
“Raheem played in the first half to score a goal," said the boss.
“He showed us the energy we need. The way he played the first half showed us what we should do, where we should go and we did it.
“The only person in the first half who was aggressive was Raheem. In the second half we imitated him.
“What I liked the most is after scoring three goals against Atalanta, everybody talks in the media how good you are.
“Usually the next game you play like 'how good am I' (letting the praise go to your head).
“He was the complete opposite. That is our strength as a team in the last years together. I am so proud of Raheem."
Guardiola added: “Respect and credit for Aston VIlla. We have to play 90 minutes not just 45.
“If we play at the level we did in the second half we will be there until the end of the season, I am sure of that.
“If we play like in the first half we will be near the relegated positions far away from leading the table."