United had a second-half lead through Diogo Dalot before Soungoutou Magassa struck an 83rd minute equaliser.
Keane told Sky Sports: "You try and deal better being one up against a team in the bottom three and Everton with 10 men. If you can't deal with that, how can you deal with being a team in the top of the table?
"If they are anxious, you worry why they are playing for Manchester United and what they are fearful of. Fearful of West Ham, why?
"I've watched the games closely, the lack of quality and intensity. They got two goals against Palace but they defended like a pub team.
"Tonight, you give United praise before the game and they can go fifth. This team is not ready to go fifth – fifth in the league!"
Keane also said: "When you look at the squad, considering the money that has been spent, they lack strength in depth, particularly in the attacking areas. Defensively and in midfield, there are huge questions.
"I wouldn't trust or believe in this team that they can get results. I look at Mason Mount when he came on, he was like a schoolboy out there.’
He added: "United have scored just one goal in their last two home games - they're just putting themselves under pressure. Every time I watch this United team they just disappoint me. They weren't clinical, they weren't nasty enough to get the job done.
"I think the standard of United's play in the last three or four games has been desperate. Really, really poor. Again tonight they seemed frightened to get the job done. Frightened to go up to fifth.
"My goodness, we're talking about fifth here by the way, not the top of the league."