The Northern Irishman refused to criticise his players despite a subdued showing in 2-0 league defeat at Arsenal on Saturday night.
Arsenal put five points between the two sides thanks to goals from Santi Cazorla and Aaron Ramsey, with Rodgers admitting Arsene Wenger's men overran Liverpool in midfield.
"They are winning the race," Rodgers said.
"These 10 games we've all played, people talk about it being early, but you don't get them back.
"You don't get to play them again so you've got to claim the points.
"At the moment we're on 20 points and they're on 25.
"The great thing is there's lots of time left to gain those points back, but at this moment in time they are high in confidence, playing well and they will be pleased with the win.
"There's always disappointment when you lose a big game. We were happy when we beat Manchester United earlier in the season.
"After 10 games there's always a good assessment of where you can go.
"Look at Chelsea's squad, at Arsenal's squad even with the players who are out, and look at Manchester City's.
"So for us to be where we are, that's where we want to be, we've shown that we're going to have a fighting chance."
Rodgers admitted it will take time to build up a squad to match Liverpool's rivals, but is more than satisfied following their strong start to the league campaign.
"We want to stay there. We know we're trying to build something here in the depth of our squad, and the nature of our game," he said.
"Without a major investment that just takes a bit of time.
"But listen, they're a team here, I watched them (Arsenal) against Napoli and they were brilliant, and that's top-end Champions League.
"They are a very good side with very good players, and for us we're playing catch-up.
"I think we've had a terrific start, but when you lose a game there will always be an analysis that will maybe be negative.
"I can only be positive with what I've got, because they've given me everything."
The Liverpool boss also hailed 21-year-old Brazilian playmaker Philippe Coutinho's second-half impact at Arsenal in his first outing since undergoing shoulder surgery in mid-September.
Rodgers said: "He's a wonderful player. He's a big talent for just under £8million.
"He's remarkable: his feet, his talent, his ability on the ball.
"He was great when he came on and of course we'd have loved to have started him.
"But he's only really come back into the fold and got the clearance medically in the last few days."
Rodgers confirmed right back Glen Johnson had been admitted to hospital suffering a 'freak illness' just before kick-off at Arsenal - but expects a quick recovery for the England defender.
Despite an uncharacteristic off-the-boil showing from Steven Gerrard, Rodgers backed the Liverpool captain to shrug off a minor hip complaint and handle the fixture load with England's friendlies against Chile and Germany later this month.
Rodgers added: "He took a knock towards the end, with his hip.
"I'm not sure the complete diagnosis on it.
"Stevie's been brilliant for me, it was a tough game for him, but we'll assess his injury and see where he's at.
"Roy (Hodgson) has always handled Stevie really well, both when he was Liverpool manager and now the player is England captain, so I'm sure that will be fine."
Come on now Brendan, we are not playing catch up as we are not going to win the league.- marrowak