Sterling expects Liverpool to push Manchester City all the way in title race
City trail the Reds by two points but have a game in hand.
But with City having played a game less, their destiny is in their own hands.
Sterling feels the title rivals will continue matching each other stride for stride over what promises to be an exciting run-in.
“Yes, 100 per cent, the way Liverpool have been playing it will go down to the wire,” he said.
“I don’t see us slowing down now. Liverpool have a great squad, great self-belief, but so do we.”
Sterling scored twice to put City in control, but only after he missed a glorious chance to give them the lead.
“I tried to be a bit too clever with the first one,” he admitted. “But the game is 90 minutes and it was still 0-0, so I knew there would be more chances.
“When I was younger you always want to score your first opportunity and sometimes it doesn’t happen like that. You don’t beat yourself up.
“There’s 80 minutes left, you just have to be ready for the next opportunity. That’s the mentality, just keep going and the chance will come.”
Luka Milivojevic gave Palace hope with a free-kick nine minutes from time, but
substitute Gabriel Jesus wrapped up a ninth straight win for City in stoppage time.
“We always knew coming here in the past that it’s a difficult place to come,” said Sterling. “We got two goals but knew we couldn’t switch off.
“We kept pushing and we were glad to get the third goal. We knew we had to be on it from the first minute.”
It was a tough afternoon for Palace and in particular Christian Benteke, who started his first game since February 9 and played the whole 90 minutes.
The striker told the club website: “I am happy. It has been a tough season with injury but the main thing is for the players to control what they can control.
“I am always available for my team-mates and I work hard in training to be where I am. I will keep pushing myself until the end.”