Mr Trichet hands over the reins of the ECB to the Italian central banker, Mario Draghi, warning that there should be no repeat of last week's deal to reduce Greek debt.
He also said that Greece should have come under greater scrutiny before it joined the euro.
Mr Trichet, told the BBC that the agreement was a one-off and other countries should honour their debts in full.
As the head of the European Financial Stability Facility Klaus Regling meets with Chinese officials in an effort to boost the bailout fund, Mr Trichet denied that eurozone countries are going "cap in hand" to China and said the move was "absolutely normal".
As ECB President, he has overseen some of the most turbulent years of the eurozone.
Meanwhile, China 's President Hu Jintao has pledged "active support" for debt stricken Europe and said it could work through its current crisis.
Hu said that China is convinced that Europe has the wisdom and the competency to overcome the current difficulties.
