Palace took plenty of pride from Saturday's battling 1-0 defeat at Manchester City, but they returned home with no points and only goal difference is keeping them above the drop-zone.
Fellow strugglers Norwich head to Selhurst Park on Wednesday and Palace could gain some much-needed breathing space, with a win lifting them above the visitors in the Premier League table.
"The next game is massive," said Bannan.
"We will be judged on the games against the teams who are around us and Norwich at home is one we expect to get something from.
"With the home crowd behind us and the confidence we have in the squad at the minute we have every reason to look forward with confidence."
The south Londoners were expected to suffer a heavy defeat at City and Bannan believes the team's resolute display has proved they have the stomach for a survival fight.
"A lot of people had written us off and were expecting a Manchester City goal glut," said the Scottish midfielder.
"But we showed we are capable of holding our own in this league.
"It wasn't backs to the wall. We managed to stop them hurting us and when they scored we were on top.
"Joe Hart has pulled off some great saves so it is a bit devastating that we ended up with nothing."