United held a 3-1 lead at Leicester with just under half an hour of the game remaining, only to lose the game by five goals to three.
"It shouldn't be possible [to lose like we did], but it still happened," Van Persie told Fox Sports News. "We have to deal with it.
"We had a proper look at it next day. Sometimes it was a bit confronting and it was a long meeting. One hour something. We went from there, started again this week [and have put] a couple of really good sessions in. Everyone feels ready to face West Ham.
"When you look at the defensive mistakes, it starts somewhere else. That's where we looked at as well. It's not just the one mistake which happens. There's a mistake before the mistake and before the mistake, maybe positional wise."
United return to Premier League action on Saturday with Sam Allardyce's West Ham United the visitors at Old Trafford.