Carragher said: "The last two home results have been disappointing and to only take one point from them is certainly not good enough. But we're still in there fighting and with a chance of finishing fourth.
"I don't think we were as poor on Saturday as we were against Charlton but it wasn't our best performance by a long way. We set higher standards than that and we expect more from ourselves.
"The fans were frustrated at the end but then so were we. I have no problem in them booing us off. They pay a lot of money to come and watch us and if we don't do the business then they have a right to have their say.
"We have four games left, of which two are away at Man United and Birmingham. On paper they look like tough matches for us, but things don't always work out as you'd expect. We've found that out over the last two home games. Who's to say we can't go to Manchester United on Saturday and win? We'll certainly give it our best shot."