He said the attack on Monday was "revenge for the [suspected US] drone attacks in Pakistan".
At least 100 people were injured in the Lahore attack, which only came to and end when security forces arrived to overpower the fighters.
Security officials said at least four of the attackers were killed and at least three were seized.
Rehman Malik, Pakistan's interior minister, said that the fighters involved in the attack came from the southern province of Waziristan, which is the stronghold of Pakistan's Taliban and said to be a sanctuary for al-Qaeda, and that one of them men captured was an Afghan.
Rashid Qureshi, a Pakistan security analyst based in Islamabad, said that the attack had reflected badly on Pakistan's government.
"This is definitely a big embarrassment for the government and also for our intelligence agencies and security apparatus that ... the capital of the largest and most prosperous province of Pakistan [the Punjab] was held hostage for eight hours and what was attacked was a law enforcement agency," he told Al Jazeera.
Mehsud, who has a $5m bounty on his head from the US, leads the Tehrik-e-Taliban Pakistan, or Movement of Taliban Pakistan, a loose umbrella group of factions which has carried out attacks across the country.
The US says the group sends fighters across the border to fight Western forces in Afghanistan.
Al Jazeera's Kamal Hyder, reporting from Lahore, said: "Pakistan has been saying all along that the problems within its territory are a direct consequence from the escalation of the war in Afghanistan where Nato and US fores say they face an up hill task.
"Whenever there is conflict in Afghanistan, it has a direct consequence on Pakistan because of the continuity of the tribes living on both sides of the border."
Funeral prayers were said for the dead on Tuesday, with security forces deployed on rooftops around the Lahore compound to ensure security.
The Lahore attack came less than a month after a dozen gunmen attacked Sri Lanka's cricket team in the city, killing six police guards and a bus driver.
Meanwhile, Pakistan's supreme court suspsended a court ban on Tuesday barring Nawaz Sharif, the leader of Pakistan Muslim League-N (PML-N), and his brother Shahbaz from holding elected office and restored their government in Punjab.
A statement released from the office of Yousaf Raza Gilani, Pakistan's prime minister, said he "hoped that with today's decision, all political forces in the country would work towards greater political reconciliation."