Lucas Leiva has encouraged Liverpool supporters to take maximum satisfaction from the Reds' faultless beginning to the 2013-14 campaign after Manchester United were beaten at Anfield.

Brendan Rodgers' team have won each of their three Barclays Premier League matches and downed Notts County after extra-time in the Capital One Cup.

Players and manager alike have warned that a lot of hard work remains this season, but Lucas believes the fans have every reason to enjoy an international break with Liverpool top of the league.

"I don't think it's dangerous for the fans to get a bit carried away after a win like this - they should celebrate," said the Brazilian.

"It's a great start. We can't deny that. That's the way we wanted to start.

"But for the players, we need to keep our calm and keep our focus as it's a long, long journey until the end of the season.

"For sure, it's a great start and much better than last season. We just need to keep our focus and try to play every game like a final.

"There's a greater belief among us now. We all believed previously, but now we have a stronger team.

"We've always said the main target this season is a top-four finish as we all want to play Champions League football.

"If we keep going like we have done now, then it's going to be a great season. But the fans just have to celebrate, and if they have the belief then they will support us even more."

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Liverpool were defeated twice by their great rivals United in 2012-13 but controlled the encounter on Sunday as the Reds claimed three points through an early Daniel Sturridge effort.

Lucas continued: "We know the way we have to play for a win, even if it's not the best football, especially in the second half against United when we had to defend a lot.

"We have kept three clean-sheets in three games so that shows we are solid at the back, and the goals will come for sure because we have quality players in attack.

"We had a lot of draws last season against the top teams. It doesn't mean we were worse than them. Maybe we couldn't get the three points we wanted against the big clubs, though.

"Sunday was a big test for us. It showed we were capable of fighting against teams like United.

"We got the win, and it was a nice message to the fans that this group believes we can play against anybody."

After guiding his team to the division's summit on Sunday, Rodgers further strengthened his options with three signings on deadline day - Tiago Ilori, Victor Moses and Mamadou Sakho.

Lucas welcomed the increased competition provided by the new trio and pledged to help the recruits settle quickly and make an immediate impact at Anfield.

The 26-year-old added: "With a few more players coming in, it will make the squad stronger and make everybody ready to compete for a place in the team.

"And that's important for every single team. We have given the manager a lot of options to change the team around if he feels he needs to.

"Sometimes the players on the bench are the key to change the game.

"The squad is getting stronger and the team spirit is there, we just have to keep doing what we have been doing.

"It's always positive that you have a good transfer window. When you let a lot of players go like we have done, it's important to replace them. The manager and the people in charge have done that.

"We just need to make sure these players coming in feel comfortable, because if you feel comfortable then the easier it is to perform."