India also asked the US to sensitise the authorities at all its airports to cultural and religious sensitivities of foreign diplomats.
Lu was summoned by Javed Ashraf, joint secretary (Americas), to his office in India's external affairs ministry in South Block.
Shankar was subjected to the security search at the Jackson-Evers International Airport Dec 4 when she was to board a flight to Washington after attending a function at the Mississippi State University.
"We made it clear it was unacceptable," a source in the external affairs ministry said.
According to the Jackson Clarion-Ledger, Shankar was singled out from a group of 30 passengers and pulled aside. Witnesses told the paper that she was chosen as she was wearing a sari, and was patted down despite her diplomatic passport.
Ashraf conveyed to the US diplomat that despite the fact that the mission has followed the state department's guidelines for expedited clearance for ambassadors and Shankar had presented her diplomatic identity, the envoy had to undergo enhanced security checking because “as we have been informed she was wearing a sari".
The US diplomat was told that India understood and respected everybody's security procedures, but also expected that normal diplomatic privileges and courtesies are extended to ambassadors and Indian diplomats.
"India respects diplomatic privileges of foreign diplomats in India and extends diplomatic courtesies to them. Such incidents naturally lead to call for review of privileges and facilities extended in India," the US diplomat was told.
Alluding to External Affairs Minister S.M. Krishna's comments on the incident, Ashraf made it clear that such incidents are "unacceptable".
The US deputy chief of mission was told that it was contrary to normal diplomatic practice and was inconsistent with excellent relations India and the US enjoy, said the source.
"We expect that the State Department and the US Transportation Security Administration (TSA) would sensitise all its agents at all airports to cultural and religious sentiments of foreign diplomats," Ashraf told Lu.
Amid an uproar in India over the "pat down" frisking of the Indian ambassador, Washington has promised to see what could be done to prevent such incidents.
"We obviously are concerned about it," US Secretary of State Hillary Clinton said Thursday as India reacted strongly to Shankar being pulled out of an airport security line for a pat down in Mississippi despite being told of her diplomatic status.
"We will be looking into it and trying to determine both what happened and what we could do to prevent such incidents in the future," Clinton told reporters at the State Department.
The government decided to summon the US diplomat after opposition parties like the Bharatiya Janata Party clamoured for an apology from Washington over the incident.
Earlier, the TSA had asserted that diplomats are not exempt from the searches.
Shankar "was screened in accordance with TSA's security policies and procedures", spokesman Nicholas Kimball said in Washington. A number of factors could prompt a pat-down search, including bulky clothing, but he said the agency did not generally discuss specific cases.