The Aam Aadmi Party, which finished a distant third, too, made similar allegations against the Congress party. AAP nominee Maj. Gen. (retd) Suresh Khajuria accused the Congress party of using "undemocratic means" to win the byelection.
None of the parties offered any evidence to support their allegations.
Congress' Sunil Jakhar won the bypoll necessitated following the death of BJP MP from the seat, Vinod Khanna, in April. Mr Jakhar defeated BJP's Swaran Salaria by over 1,90,000 votes.
Punjab BJP secretary Vineet Joshi alleged the Congress misused the official machinery to win the bypoll.
"They won by misusing the machinery. Everyone knows that even the sarpanches owing allegiance to the BJP and the SAD were warned that they will be dealt with strictly if the two allies got a lead in their respective areas in the bypoll. Civic body officials, too, were warned," Mr Joshi alleged.
Senior Shiromani Akali Dal leader Prem Singh Chandumajra said: "It is not a victory of democracy, but it is victory of government machinery being misused."
Mr Chandumajra said, "the fact that the poll percentage in a LS bypoll was as low as 56 per cent raises eyebrows. In a general election, this percentage remains over 75 per cent. The poll percentage for bypoll should have been over 80 per cent, but it was just 56 per cent. This means a lot of people were under some kind of threat that they chose to stay away".
AAP's state unit president Bhagwant Mann said his party accepts the mandate and will introspect the reasons for the defeat.
Contrary to Congress party's claims, Mr Mann said the bypoll outcome would not set the tone for 2019 general election.