Meaning : Acknowledge faults or shortcomings or failing.
Example :
I apologized for being late.
He apologized for the many typoes.
Synonyms : apologise
Meaning : Defend, explain, clear away, or make excuses for by reasoning.
Example :
Rationalize the child's seemingly crazy behavior.
He rationalized his lack of success.
Synonyms : apologise, excuse, rationalise, rationalize