Brendan Rodgers believes his Liverpool side can confound their critics by not only chasing down fourth-placed Everton but also catching Manchester City in second.
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Rodgers argues that his players have been "hammered" unfairly by pundits this season, and insists that his side's performances have been better than results suggest.
Liverpool have spent virtually the entire campaign in the bottom half of the Premier League table, but climbed to their season's high of tenth place by winning 3-2 at West Ham last Sunday.
That result came after a 1-0 home victory over Southampton the previous weekend, and marked the first time Liverpool had recorded back-to-back league victories since Rodgers took over in June.
Liverpool host Aston Villa in the Premier League on Saturday before Fulham visit Anfield the following weekend.
With trips to Stoke and QPR over Christmas followed by a New Year home clash with Sunderland, many Liverpool fans believe the club have a great chance to close the four-point gap between themselves and neighbours Everton, who occupy the fourth and final Champions League qualification place.
But Rodgers believes his side can, over the remainder of the season, also cut the 11-point gap between his side and Manchester City in second.
He said: "I've heard lots of people talk about Liverpool. Everyone's got their opinion, and I understand that because of the standards the club set in the 1970s and 80s. I'm well in tune with that but, for a club that's supposedly been very poor, we only lie four points off that top four position. And for me, the ambition is to grow higher.
"We're 11 points off second and that can all turn round very quickly. We need to get consistency. That's what we've got at the moment.
"If we can keep showing the motivation and commitment, then this sequence of games are opportunities, but it's no good looking at Fulham next week just yet. We've got to take care of Aston Villa this week."
Rodgers, who welcomes back top scorer Luis Suarez from a one-match ban for the Villa game, is adamant that an upturn in results has been coming for some time.
Having made their worst start to a season in 100 years by collecting two points from their opening five games, Liverpool have lost just one of 11 league matches since.
Rodgers added: "I've never had any complaint with the players. They've been brilliant since the first day I walked in here. They've been hammered throughout the season, left, right and centre, by a number of people, but I was quite calm because I see them every day, and their focus and concentration has been first class.
"I'm just happy for them that they're getting the rewards for their hard work. It's just steady progress that we're making. We're not enough halfway through the league season. But for us, our focus is on the next game."