The Norwegian believes Allardyce has turned the fortunes of the club around since taking over from Paul Ince in December.
"Since the gaffer has come in, we have done really well. Five wins, four draws and one loss. That is very good," said Pedersen.
"We have been keeping things simple. The manager has been keeping things organised and he has been good for us.
"If you are under the relegation line, you are under the relegation line and you are going to get relegated. It was hard after the Wigan game.
"He is very experienced, he has good results and he has dragged us the same way.
"He has kept things simple. He knew we could not take any chances and sometimes we have had to play a little ugly. He is so organised. He came in and has done a really good job and we are saved now.
"I think we are safe now but that doesn't mean we stop, does it?
"We want to finish as high up as we can and we will be confident of getting results."