Benitez's third-place side are 11 points behind leaders Manchester United with just one game in hand - but they are only four points behind champions City.
The Czech No 1, 30, said: "You need to get a run of games where you get three points. That is the only way to close the gap and take advantage when the other teams slip.
"We have closed the gap on City and hopefully have opened the gap on the teams behind. City losing was another positive thing. Getting more points against Everton would be a really big win."