"There would be internal tensions within the UPA following today's results," Mahajan told reporters in Mumbai.
Mahajan said BJP would, "...like to get the post of deputy chief minister in Bihar." "This time, we will not have to depend on unwanted elements," he said.
The 15-year reign of Rashtriya Janata Dal chief Lalu Prasad Yadav ended because " people realised that the cards of social justice and emotional appeal don't work," Mahajan said.
"We expected a simple majority in Bihar, but such a big win was unexpected," he said.
On Maharashtra Congress leader and Revenue Minister Narayan Rane winning the Malwan assembly bypoll on Tuesday, Mahajan said, "There will now be an alternative centre of power in front of Chief Minister Vilasrao Deshmukh."
The Shiv Sena's loss in Malwan and in Mumbai North-West would not have any impact on the Sena-BJP alliance, Mahajan added.