In the resignation sent three days back, he took moral responsibility for losing his seat and the party's not so outstanding performance in the Congress-ruled state.
The Congress has won eight of the 13 seats. The Akali Dal and the BJP won two seats each while the Aam Adami Party (AAP) won one seat.
In his letter, Jakhar said he was unable to retain his seat despite the best support by the Congress President, General Secretary Priyanka Gandhi and Chief Minister Amarinder Singh.
"Everyone supported me fully and put in their best for me but I was unable to defend my seat. In such a scenario I cannot continue as state chief. I feet a moral responsibility to quit," said Jakhar, who lost by over 77,000 votes.
The BJP-Akali Dal fielded 62-year-old Deol from Gurdaspur, the seat represented four times by yesteryear actor Vinod Khanna, who died in April 2017 due to cancer.
Jakhar, 65, won the October 2017 by-election with a margin of 1.92 lakh votes.
The by-election followed Vinod Khanna's death.
Veteran actor Dharmendra, who had campaigned and sought support for his actor-turned-politician son Deol, said he was a friend of Sunil Jakhar's father, the late Balram Jakhar.
He said if he had known that his son was contesting against Sunil Jakhar, he would not have allowed his son to contest against him.
As a BJP candidate, Dharmendra refused to contest against Balram Jakhar from Churu in Rajasthan in the 2004 Lok Sabha elections. He contested from Bikaner.
Dharmendra won from Bikaner while Congress candidate Balram Jakhar lost from Churu.
In 1991, Dharmendra campaigned for Balram Jakhar in Sikar.
Dharmendra hails from Sahnewal town near Punjab's industrial town Ludhiana.
( With inputs from IANS )