The run encompasses wins against Sunderland, Liverpool and Brighton, plus, most recently, draws against Nottingham Forest and Tottenham Hotspur.
In the second part of his pre-match briefing with journalists at Carrington, Amorim was asked how far he feels the Reds can extend that streak.
"We need to think to be six games unbeaten," the boss said, in response to a question about how far the run can go. "But then unbeaten is not enough.
"I came from these last two games [against Forest and Spurs], especially the last one, very frustrated.
"So, for us, it's not enough.