Speaking to Sky Sports after the win, Benitez said that Newcastle already have the infrastructure and fan-base to be successful in the top half of the Premier League but must invest in the transfer market to be more competitive - indicating that he wanted to be promised backing in the transfer market before he signs a new deal.
Newcastle have four games left and have to play Southampton, Brighton and Fulham - all teams below them - along with Liverpool. We have the city, we have all the potential. We have the city, we have all the potential, we have everyone in Newcastle supporting the team, it's massive. "But we have to do things right".
"You can do everything right with your tactics, but the other team has one player that can make the difference".
Salomon Rondon nearly gave Newcastle the lead midway through the first half with a ferocious 30-yard free-kick that cannoned back off the woodwork.
Leicester remain seventh on 47 points, while Newcastle moved up to 13th on 38 with their first away win since December.
It was a well-worked goal by the away side that started with Miguel Almiron running at the Leicester defence which left Ritchie unmarked out wide.
Harvey Barnes was a constant threat for Leicester and he surged past two defenders for a shot which Dubravka was equal to.
Forward Ayoze Perez scored the victor in the 32nd minute when he headed in from Matt Ritchie's cross.
The Magpies had numerous chances to get a second goal, but also never seemed like conceding a goal as they restricted Leicester to a lot of passes around the box.
"The speed of our passing in particular can be much better".
Perez was denied by a fine save from Schmeichel in a frantic finale.
Set-piece specialist James Maddison wasted a free-kick from a good position in the 75th minute and Jamie Vardy fluffed his lines later still with a miss that summed up Leicester's lack of clinical edge.
The last opportunity for a Leicester leveller came and went in stoppage-time when Tielemans appealed in vain for a penalty after going to ground when a cross reached him at the far post.
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