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Rafael Benitez is targeting victory over former club Liverpool after seeing Newcastle take another small step towards safety.
The Magpies edged to within two points of Norwich after a hard-fought 1-1 draw with Champions League semi-finalists Manchester City at St James' Park, and might even have snatched a priceless win - which would have lifted them out of the Barclays Premier League drop zone - at the death.
However, they will head for Anfield on Saturday knowing only a continuation of their improved form - they have taken four points from the last six on offer - will give them any chance of getting out of trouble.
Benitez, who led Liverpool to Champions League glory in 2005, said: "We have to try to win every game, it doesn't matter where.
"My connection with Liverpool is obvious, it's quite good, but hopefully they will do really well in the Europa League and we can get three points in the Premier League.
"At the moment, it's true that we are doing well, so hopefully the game away against a very good team like Liverpool, we can see the same things. But you never know.
"What we have is belief. We believe now that we can fight, we can beat anyone and in the next games, we have to show that."
The Magpies, who had not beaten City in the league in 18 attempts dating back to September 2005, came desperately close to doing so on a night when Sergio Aguero's 100th Premier League goal - which should have been disallowed for offside - gave the visitors a 15th-minute lead.
Vurnon Anita's first strike in more than two years levelled it and substitute Georginio Wijnaldum was denied a stoppage time winner by keeper Joe Hart.
Asked if he was pleased, Benitez said: "Yes, pleased - very pleased if Gini had scored the goal. But really pleased because the reaction of the players, the way that we were fighting, the passion, the commitment, the relationship with the fans, everything was so positive today that it was just a pity that we couldn't score the second goal.
"It could be better, but it could be worse because you are playing against a team that is in form, it's in the semi-finals of the Champions League and at the top of the Premier League.
"Before the game, I wanted the three points; after conceding the goal, to see the reaction of the team, one point could be fine; after Gini's chance, I was a little bit upset, but you have to be pleased in the end."
Opposite number Manuel Pellegrini was disappointed with a performance which fell far short of the standard set in Saturday's 3-0 win at Chelsea and a result which left his side 12 points adrift of leaders Leicester and seven behind second-placed Tottenham.
He said: "That was not the same team as on Saturday, without any doubt. Maybe we couldn't recover so soon after three days to have the same pace that we had against Chelsea.
"We knew also before the game that it was going to be a very tough game because Newcastle are playing not to be relegated next season. They had just won their last game, so it was a difficult game as we expected."
Pellegrini was at least able to revel in Aguero's achievement with only Newcastle old boy Alan Shearer having reached a Premier League century in fewer than his 147 appearances.
He said: "I am happy for him because it's not easy to score 100 goals in the amount of games that Sergio did it.
"He's second in the history of the Premier League, so I am happy for him and I hope he will continue the same way until the end of the season."