Everton won the match after a 87th minute goal by Louis Saha, his first goal for the club.
Moyes said: “It wasn’t a good performance but the result was really important to us, that’s two wins in a week now.
“It was always going to be tight, Fulham don’t concede many goals. We’ve kept another clean sheet but we needed a bit of good fortune at times.
“We were a bit wasteful at times in the first half but in the end we got there.”
