City started the campaign as Premier League title favourites after boss Pep Guardiola spent £220m over the summer revamping his squad.
His side have picked up four points from their opening two league games, but winger Sterling believes it should have been six.
City dominated in winning 2-0 at Brighton before drawing 1-1 at home to Everton on Monday night.
Their three goals have come from a total of 33 efforts.
And Sterling says that’s not good enough.
“We’ve just got to be a bit more clinical,” he said. “That’s what’s missing. We’ve got to move on and go again next week.”
The 22-year-old admitted he was frustrated with himself for missing a good chance against Everton before equalising with eight minutes to go.
“I was really disappointed because I had a chance before I scored, and it’s one of those. I’ve just got to hit the target.
“Luckily enough, I got a second chance and put it away. But it’s those little vital moments that are going to count.
“It’s the chance before that, not just the equaliser. If I score that chance, then we win the game.”
But even though City are not making their chances count, Sterling believes they are showing the character of champions.
They had to play more than half the match against Everton with 10 men after full-back Kyle Walker was controversially sent off for a dubious second yellow card.
“We’re always up for the work,” Sterling said. “We always work for each other.
“It’s always great to see, when you go down to 10 men, the boys’ work running and keeping the ball and attacking on all fronts. It’s a credit to the boys and the gaffer with his tactics.
“In the second half, being down to 10 men, we didn’t stop trying to play football.”
City cannot appeal against Walker’s sending off, as it was for two bookings, and yellow cards can only be overturned if there is a proven case of mistaken identity.
However, midfielder Fernandinho has accused Dominic Calvert-Lewin of taking a dive to get Walker sent off.
“It’s tough to say something about a referee’s decision, you have to be careful,” the Brazilian said.
“But we are in the Premier League and it is so demanding and when you have some players who dive and they are so soft, it is a little bit weird.”
