The Merseyside club have collected 10 points in those games, following a draw with leaders Liverpool and wins over top-four contenders Chelsea, Arsenal and United and Silva said the hard work had to continue.
"We have many things to keep fighting for. It is important for us to keep this run, to keep playing well and achieving good results and to finish the season in a good spot," Silva told the club's website http://www.evertonfc.com/news/2019/04/21/manager-reaction.
Victory over United was Everton's biggest against the 20-times league champions since a 5-0 win in Oct. 1984 and left them in contention for a Europa League spot.
"We have to keep fighting, to prove our quality in every match," Portuguese Silva added.
"But it's important to give this good feeling to our fans. I want our players to enjoy the moment and our supporters also. I want our players resting... and preparing to work really hard to get ready for the next game."
Everton, who have 49 points from 35 matches, visit Crystal Palace on Saturday before hosting Burnley on May 3. They play their final game at Tottenham Hotspur on May 12.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Amlan Chakraborty)
