The Addicks picked up draws against high-flying Nottingham Forest and Blackpool before the international break despite missing the likes of Chris Solly, Johnnie Jackson and Yann Kermorgant through injury.
They head to Blackburn next weekend lying just a place and a point above the drop zone but Hamer is confident they can stay clear of trouble.
"Character and spirit is what you need when you've got a thin squad," he said.
"We know we haven't got the highest budget in the league or the biggest squad but one thing we have got is a lot of team spirit and we've shown that over the last couple of years.
"We've just got to pull together. It's tough when your squad is thin, especially at the moment when we have key players out and we've got to pull together.
"I think we've done that in the last couple of games. But that's what we've got to do, we've got to keep plugging away and hopefully the results will come."