Craig Morgan and Ben Pringle have rejected new contracts at Rotherham and will leave the club on free transfers.
Saido Berahino can leave West Brom "if the deal is right", says manager Tony Pulis.
Ireland were thrashed 6-1 at home by Germany in their recent World Cup qualifier reigniting criticism of the 73-year-old after a poor showing at Euro 2012.
And having belatedly received the backing of the Football Association of Ireland, Trapattoni is looking to the future once again.
Asked if defeat by Greece on Wednesday in Dublin would have the critics calling for his head again, Trapattoni said: "I don't think so.
"People forget the victories. In my life, what I have done until now, and now also with this team, is improve teams. That is the life of the manager.
"You can lose because of a referee's mistake or because of another mistake. For us, it's not a great problem. For me, it's no great problem.
"Maybe I am a little bit presumptuous, but I know how good a job we have done in the last two or three years.
"We have changed the team, discovered other players and we achieved qualification for the Euros, so I think we have done our jobs well until now."