The Cottagers withstood Arsene Wenger's side for long spells until a double from Santi Cazorla condemned them to a 2-0 defeat at Emirates Stadium
Santi Cazorla was on the end of a slick passing move to put the hosts ahead shortly before the hour mark at the Emirates Stadium on Saturday before doubling the advantage from 20 yards five minutes later.
Despite being pleased with his side's first-half display against the Premier League leaders, Meulensteen believes his players could have defended better in the build-up to the opener.
"I was very pleased at halftime, to say the least," he said. "I thought Arsenal started strong, but we got into our stride. We knew that we needed to have a very solid defensive performance if we wanted to get something out of the game.
"I thought, on the back of the Norwich performance in FA Cup (a 3-0 win), I stuck to the same defensive line with the same goalkeeper and I thought we looked very comfortable in the first half at times."
The coach praised Arsenal, saying his side couldn't afford to make the mistakes it did against such a good team.
"The quality of player that they've got, if you have moments where they are moving the ball around quickly and you just switch off one moment and don't track runners, they can hurt you and that's what they did," he said. "It was a typical Arsenal goal, but we clearly worked hard this week on making sure you keep defending the danger area, but especially make sure you stay with the runners rather than following the ball. That's what happened in the first goal."
The result leaves Fulham one point clear of the bottom three in the Premier League.