"We will ask for his (Ashraf's) resignation in the meeting which is due to take place before March 28," said Senator Mohammad Enver Baig, a member of the senate standing committee on culture, sports, youth affairs and tourism.
"You lost miserably to a country like Ireland. There is nothing to compensate and the chairman must resign and go back to the United States," Baig said.
"The way the team has lost is the most disgraceful performance since the World Cup started. The entire nation is shocked."
Baig said Ashraf had no experience to head the Board and his "one man show" type of management had resulted in the "shameful defeat."
"He is a crony of (President) Pervez Musharraf and the way he (Musharraf) is running the country, the cricket board is also being run in same manner. It is a one-man rule everywhere," Baig said.
Former cricketing great, paceman Sarfraz Nawaz, said the defeat was "unbearable" for him.
"I am speaking with deep pain and this shock is becoming unbearable for me," Nawaz said.
"The captain, coach and the entire team should be held accountable," he said.
Nawaz demanded that those responsible for defeat must be "fired".
The former bowler refused to put any blame on the umpires.
"It seemed that the umpires also wanted that Pakistan should win, but the body language of the team reflected that they wanted to lose," he explained.
In the central Pakistan city of Multan, skipper Inzamam-ul-Haq's home town, angry youths held a protest rally, chanted slogans which called for more than just resignations.
"Death to Bob Woolmer (the coach), death to Inzamam, death to Nasim Ashraf -- police should arrest them", the mob shouted.
The win put minnows Ireland in the lead of Group D on three points, one more than West Indies and two ahead of Zimbabwe (who play on Monday) leaving Pakistan at the bottom of the table with no points.