Fulham were fortunate to go into the half-time break just 1-0 down after Leon Osman's early opener as Roberto Martinez's side dominated from the outset.
However, the Londoners came out strongly in the second period and deservedly drew level through Dimitar Berbatov's 67th-minute penalty, before Seamus Coleman, Gareth Barry and Kevin Mirallas scored to give Everton a flattering 4-1 scoreline.
Fulham therefore remain in the relegation zone after suffering their seventh defeat in eight Premier League games, but head coach Meulensteen saw cause for optimism in the manner his team played after half-time.
"Absolutely," the Dutchman replied when asked if he was encouraged by Fulham's showing at a ground where high-flying Everton have not lost a league game in 2013.
"(The scoreline) didn't reflect the actual game, especially the second half.
"We came back really strongly, put them under pressure and got the equaliser but then conceded too soon.
"The goal to make it 3-1 settled the game…(but the) second half was much, much better.
"This is just a hard defeat to take. We need to brush it off, get to the training ground and prepare for the next game."
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