Trapattoni came under increasing scrutiny during his final months as Ireland boss and eventually left the post by mutual consent last month after failing to qualify for the 2014 World Cup finals in Brazil.
However, St Ledger believes that the veteran Italian did a good job during his five-year reign and warns fans that they may miss how successful he made the national team.
"Sometimes football fans think the grass is greener on the other side and sometimes, it's not. If you look back at it, we qualified for the Euros and we hadn't in such a long time; we nearly got to the World Cup in South Africa. On this stage, it's about winning football games, and that's what we did," PA quotes St Ledger as saying.
"Obviously, there were low points - the Euros, not winning - but then to get there was great. It was great for the country, it was great for the fans. But that's gone now, it's a new era. We are going to have a new manager and it's important for every one of us as players.
"The new manager will probably be watching the game on Friday, he must have an inkling that he's interested in the job, so it's up to us to go out there and show what we can do because we all want to be on this stage playing against the likes of Germany and playing in major tournaments."
St Ledger has declared himself fit for Friday's match against Germany despite not having played since early August.