The Cottagers gave their survival hopes a huge lift thanks to a narrow victory at home to the Magpies.
Despite admitting that there is a 'buzz' around Craven Cottage following that result, Woodrow wants the players to remain focused and accumulate more points in the coming weeks.
"The boys are buzzing," he told the club's official website. "It was a great result but we don't want to get too carried away so hopefully we can push on and try and get some more results.
"We don't go into any game thinking we're going to lose. We've got some good games coming up at home so if we play like we did on Saturday I don't see why we can't stay up."
Fulham, who are four points adrift of safety at the bottom of the table, return to league action on Saturday with a trip to Manchester City.