Liverpool manager Brendan Rodgers said his side's stirring display in their League Cup semi-final first leg with Chelsea had convinced him of their ability to win the tie.

A dazzling solo goal by Raheem Sterling earned Liverpool a 1-1 draw on Tuesday after Eden Hazard's penalty had put Chelsea ahead and the home side would have prevailed had it not been for the reflexes of visiting goalkeeper Thibaut Courtois, who produced a number of excellent stops.

Hazard's away goal gives Premier League leaders Chelsea a slender advantage ahead of next week's return leg at Stamford Bridge, but Rodgers said that his team will approach the game with no fear.

"It was a big performance from us," said the Northern Irishman, whose side have lost only once in their last 15 games in all competitions.

"I think they know that they were moved about the pitch tonight (Tuesday). The space that was opening up for us -- we got the goal and they really had to hang on there.

"They'll be happier in terms of the scoreline, but I'm extremely happy that our performance levels are improving all of the time."

Asked if Liverpool's showing had reinforced his belief in their ability to reach the final, where they would face either Tottenham Hotspur or Sheffield United, he replied: "That's reinforced it even more.

"You see defensively how we were; really aggressive, really compact. They've got top-class players. I felt the performance tonight was a good benchmark for us.

"There is absolutely no doubt we can go to the second leg and get the result that we need."

Liverpool's late rally, which also saw Steven Gerrard hit the post, sent their fans out into an ice-cold night full of optimism and Rodgers gave them further reason to be cheerful by revealing that striker Daniel Sturridge could make his long-awaited return from injury in the second leg.

"He's really kicked on in his rehab and done really well today, so we'll see how that looks between now and then," Rodgers said.

Sterling's moment of magic arrived in the 59th minute and saw him gather a pass from Jordan Henderson, spin away from Nemanja Matic and burn off Gary Cahill before beating Courtois with a low, left-foot shot.

The 20-year-old forward was recently granted a break by Rodgers, during which he spent time in Jamaica, where he was born, and the England starlet said that the time in the sun had done him good.

"It's always good to get on the scoresheet and help the team out," Sterling told Sky Sports.

"I've felt the benefit of the break because there are times you need a bit of rest and the manager gave me some time off and it's helped."

Rodgers felt that Liverpool were twice the victims of injustice -- first when the ball struck Diego Costa on the arm inside the Chelsea box (a "clear handball"), and then when Courtois appeared to slide out of the penalty area with the ball in his grasp late in the second half.

Chelsea manager Jose Mourinho claimed not to have properly seen either incident, but was more forthcoming on his side's chances of reaching the final.

Asked if Hazard's goal made Chelsea the favourites, he replied: "I don't know really, but to play here is obviously difficult and to transform the two-leg semi-final into a one-leg semi-final at Stamford Bridge is obviously better for us because this stadium (Anfield) plays.

"People don't come to this stadium to see football; the people come to play football, to play their way. They cannot kick the ball because they are in the stands, but they come to play."

He also praised Courtois's performance and described the 22-year-old Belgian as one of the "three best goalkeepers in the world" alongside Manuel Neuer and Petr Cech -- Chelsea's second-choice goalkeeper.