Not sure who the "we" is that you are referring to, but Israel and Mossad did go after him and more or less found him. The primary problem, and the reason he wasn't captured and tried like Eichmann, is that Israel and Mossad had bigger problems at the time. Identifying and capturing Eichmann, for example, took a good deal of time, money and energy, with dozens of Mossad agents working on the case.

Israel did come close to getting him, but he managed to evade capture and go into hiding under a false name.

Around the same time Mossad was confident they had located the area where Mengele was living, Israel was experiencing a series of crises in the Middle East, which included Egypt's effort to secretly recruit German scientists to work on a missile program. Capturing Mengele was just lower on Mossad and Israel's list of priorities. In 1960, Mossad got a new head, Meir Amit, who ordered Mossad to, "stop chasing after ghosts from the past and devote all our manpower and resources to threats against the security of the state."

They prioritized Egypt and then, later, other Arab states and gathering intelligence on their weapons and military capabilities. Obviously, these threats were taken seriously and they ultimately culminated in war in 1967. Then they prioritized preventing Islamic terrorist attacks in Israel until the Yom Kippur War in 1973.

Menachem Begin took power in 1977 and ordered Mossad to focus on capturing or killing Mengele. They came close to finding Mengele again, but he died in 1979.