"We need a good away performance because I still think there is a little difference in the way we play, like to press and how we like to make it difficult for our opponents," Koeman told the club's website. (www.evertonfc.com)
"It's all about the attitude and having that in the same way when we play at home and away.
"We need to start well, start aggressive and try to score. We need a little bit more of that mentality away from home."
Everton play three of their remaining six games away from Goodison Park, starting with Saturday's trip to 13th-placed West Ham United. Koeman said his side could take advantage of the London team's woeful home record of just six league wins in 16 games.
"They have struggled a little bit and because it's a new stadium, maybe they don't feel as comfortable as they did at their old stadium. Maybe that's a reason they don't have those home performances that everyone expected."
Everton also travel to relegation-threatened Swansea City and end the season at sixth-placed Arsenal.
Koeman said this week he wanted to keep Romelu Lukaku, the Premier League's top scorer, after reports Everton were asking a world record fee of 100 million pounds ($128 million) for the Belgian international.
(Reporting by Aditi Prakash in Bengaluru; editing by Andrew Roche)
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