"The disappointment is obviously very difficult to take, but as a professional and a manager with Bolton Wanderers in the Premier League you have to accept it and get on with life.
"There are many disappointments in this life, and particularly as a manager, throughout your time but you learn to try to accept it, take it on the chin and get on with it."
However he wishes Steve McClaren well in the job.
Allardyce added: "I'm just really glad, as disappointed as I am, that it's an Englishman with Steve being the man.
"They've obviously gone for some sort of continuity and Steve has been with England for an awful long time.
"Let's face it, recently he's had an excellent record with Middlesbrough. He's got them to the UEFA Cup final and I think that may have played a little part towards it."