Moyes rues conceding late
Visitors Everton came from behind to lead through two goals from Marouane Fellaini, and appeared on course to secure victory as they dominated the second half of English Premier League match.
But Steve Sidwell struck for Fulham in injury time to level the scores, forcing Everton to return to Merseyside with just one point to show for their efforts.
"It feels like a defeat," Moyes was quoted as saying by Sky Sports.
"We controlled all the game, but gave away a terrible goal at the end.
"We had total command going into the last few minutes. We should have done more with the chances we had."
Fulham manager Martin Jol acknowledged his team were second best for much of the contest, and feels they should have done more to test their opponents.
"They dominated us in the first half and we had a real problem with their style," Jol said.
"They were hard done by, but we should have exploited more space in midfield in the first half," he said.
"It was great to see another full house here, but I didn't enjoy the game much. I don't like seeing other teams dominate here. But we never gave up and that's a compliment to the boys.
"It's good to get a little bit of luck, but I feel for them (Everton) as well. Maybe we deserved more in the games last season - now they deserve more."