Alexander the Great's empire was the largest in history by the time of his death. How did the successors to it react to Rome conquering it within a few decades?
What we must establish in answering your question is that by this point both of the larger successor kingdoms, Ptolemaic Egypt and the Seleucid Empire were on the decline. Antiochus the third had lost a decisive battle against the Romans at Magnesia and their last attempt to crush Egypt in the 160's ended with Roman intervention. The Ptolemaic Dynasty was also in sharp decline, locked in a losing conflict with the Seleucids, who themselves were suffering from severe political instability and would be plunged into Civil war between the usurper Demetrius II and supporters of the old monarch, in addition to facing a rebellion in Judea and invasion by the Parthians. Simply put, both of the successor states were far too busy with internal and external threats to "react" to the Roman conquest. In any case, they were too weak to be making any diplomatic or military moves against Rome. Please note that I know far more about the Seleucid empire then Egypt, so if someone could contribute some info on Egypt that would be good.
Sources:
"The Land of the Elephant Kings": Space, Territory, and Ideology in the Seleucid Empire by Paul J. Kosmin
"Antiochus the Great" by Michael J. Taylor
Appian and his writings on the Syrian wars