Liverpool boss Brendan Rodgers vowed not to give up on Champions League qualification after a convincing 2-0 win over Newcastle . The Reds moved within four points of the Barclays Premier League top four after goals from Raheem Sterling and Joe Allen saw off the struggling Magpies at Anfield . With fading champions Manchester City now looking vulnerable in fourth , Liverpool 's hopes - which took a hefty blow in back-to-back losses to Manchester United and Arsenal - could have been reignited . Raheem Sterling wheels away in celebration after scoring Liverpool 's opener . Rodgers said : 'The players and myself are very motivated to do the best we can . We have shown we can put results together consistently . We have important players coming back which is good news . 'But we are looking for other teams to slip up and we have to continue winning . 'There are teams above us but , as we have seen last year , there can be changes and points dropped and I think there will be changes . ' Sterling curls the ball in to the far corner of Tim Krul 's net to give Liverpool the lead . Liverpool , inspired by Philippe Coutinho , started superbly with Sterling scoring after nine minutes and several other chances being created . Newcastle rallied before the break and had a strong penalty appeal turned down but Allen made the game safe in the second half . Rodgers said : 'It was a good performance . I thought that our attacking play was very bright , we looked exciting going forward , we worked hard in the midfield . Sterling 's shot nestles in to the back of the net as Krul picks himself up from Anfield turf . 'At times our possession could have been better but we had a real attacking intent and created chances and could have scored more goals . ' The defeat was Newcastle 's fifth in succession and left them with work still to do to ensure they do not get pulled into the relegation battle . Their misery was compounded when Moussa Sissoko was sent off for what was deemed a second yellow card offence , when he caught Lucas Leiva on the ankle . Manager John Carver admitted Sissoko could easily have been shown a straight red , however . Allen secured three points for Liverpool that narrowed the gap on Manchester City . He said : 'The sending off , it could have been a straight red , I will be honest . I have said that to Moussa , I am quite straight and I wo n't defend anyone if it is indefensible . ' Asked if Sissoko could be fined , Carver said : ' I am sure there will be some kind of disciplinary procedure . I said before the game we needed to keep 11 players . ' While Carver did not complain about that decision , he was angry that Ayoze Perez did not earn a penalty after apparently being felled by Dejan Lovren . He said : 'The game hinged on a huge decision . I do n't want to be seen to be a moaner but it is fact we do n't get big decisions for whatever reasons , it could be me . I have spoken to the referee , but it does n't help me . ' Lovren clears the ball with his head as Lucas and Perez also scrap for the ball . Carver did see reason for some optimism , feeling that his side 's performance was much improved from their derby loss to Sunderland last time out . He said : ' I thought the first nine minutes we were very tentative , nervous after our performance against Sunderland . It was a bad goal to concede . 'After that we grew into the game . It is easy to crumble at Anfield but we did n't . One or two guys rolled their sleeves up . ' I think we got a response . We did n't get a result but I saw enough . 'There are lot of positives to take from the game . A lot of people expected us to get a hiding and I think we held our own for the majority of the game . '
Liverpool beat Newcastle 2-0 in the Premier League on Monday night . Raheem Sterling and Joe Allen saw off the Magpies at Anfield . Liverpool are three points behind threeth-placed Manchester City . READ : Jordan Henderson hopes Liverpool can turn up heat on Man City . READ : Rodgers will talk to Raheem Sterling about his behaviour .