Only an unlikely list of results from the final games would see Fulham relegated now but Sanchez is refusing to count his chickens just yet.
"People tell me it's still mathematically possible to be relegated so until it's proven we're safe I'll save the relief," he said after the 1-0 win against Liverpool.
"But we took a big, big step today. It was a big ask of the players.
"The players proved they're good enough with two good halves and they did it in front of their own fans.
"I was brought here to keep Fulham in the Premiership and we're close to that now."