Fulham beat Aston Villa 2-0 last weekend with an encouraging performance at Craven Cottage, which followed a spirited defeat against Tottenham.
Now Meulensteen reckons Fulham can start climbing away from the relegation zone, starting by making a spot of history.
Fulham have lost their last 20 matches in a row at Goodison Park, the top flight's longest-ever losing streak at a particular ground.
In addition Fulham have lost five of their last six league away games and have failed to score in all those defeats.
"It is a strong motivation for us," said Meulensteen. "You should always prepare yourself to win home or away. Depending on who you are up against you have to be realistic. It's a challenge but more important for us is to kick on from what we have achieved in the last two home games."
And Meulensteen is hoping striker Dimitar Berbatov, who he knew well from their time at Manchester United, can lead the charge at Goodison Park.
Berbatov looked a disconsolate figure under former boss Martin Jol, but Meulensteen is delighted with his performances in their last two games.
Meulensteen said: "I have known him (Berbatov) for many years, I have worked with him for a long, long time and football will always be about opinions. The proof is in the performances on the pitch and so far I can only be pleased with how it has been going.
"The players have responded tremendously well and that gives us a lot of confidence to go into this game against Everton.
"Every manager has his own style. My style is a mixture of where I come from in Holland, based on good possessional play but with an attacking intent. I have spent many times working alongside Sir Alex Ferguson and it wasn't any different so hopefully in time to come I can blend that style into the Fulham team, but that takes a bit of time.
"In the Christmas period, we have Norwich away, Hull away and West Ham and the cup game against Norwich. That is a challenging time. That's when you really need to utilise the qualities of the squad.
"It will (stretch them to the limit.) You need to be picking the right teams for those games.
"I have been very happy with everyone's contribution so far. The training has been excellent. The application has been fantastic. They are throwing themselves into what I throw at them.
"The basic ingredients for any performance are based on work rate and commitment. If that's not there you can be the best players in the world but you won't get results. That's what I wanted to establish first.
"You have different players with different qualities and you have to utilise all of them to the best of their capabilities."