The Toffees are now five points adrift of the top five in the Premier League, and Osman is furious with the official's decision.
"I said to the referee at the end of the game that I thought he'd had a good game on the whole but the referees have got to get the big decisions right, and that was a massive decision for us," Osman told talkSPORT. "I'm not sure how that can be a foul against Victor Anichebe when the goalkeeper runs into him and we've had a good goal taken away from us.
"It's disappointing. We were still looking to get on the coattails of them [Chelsea, Arsenal and Tottenham] and try and catch them but that [draw is] probably not going to be enough in the end.
"We've come to Anfield, kept a clean sheet and had a goal taken off us which has denied us the victory, so we're disappointed."
Everton host West Ham United in their next game on Sunday.