At least 14 were killed and 70 others injured in the attacks during Sunday services at St John's Catholic Church and a Church of Pakistan in the Lahore district of Youhanabad.
A group with links to the Pakistani Taliban has claimed responsibility.
The National Commission for Justice and Peace, which acts on behalf of the Catholic Church in Pakistan, has said security was not good enough.
Despite a 2014 order from the Supreme Court to provide security in all places of worship, Church leaders claim there was insufficient protection for worshippers.
"This order of the Supreme Court has not been implemented," the Archbishop Joseph Coutts of Kararchi said, "this new act of terrorism has cruelly shown how defenceless we are due to this neglect."
The NCJP accused the authorities and the police of failing to provide basic security for churches despite an ongoing threat of violence faced by Christian communities in Youhanabad and elsewhere.
National director Father Emmanuel Asi said: "Although [extremists] claim responsibility for the twin church attack in Youhanabad, Lahore, the fact remains that the security at the time of [the] attack were busy watching [a] cricket match rather than performing their duty of protecting the churches.
"In result of this negligence, many Christian people have lost their life and families their loved ones."
After the bombs there were violent protests with Christians taking to the streets.
Calling for calm, Archbishop Coutts in his message to Catholic charity Aid to the Church in Need said: "I particularly appeal to all Christians to voice their protests in a peaceful manner and not to resort to violence and destruction of public property, which serves no purpose.
"Once again, the state has not been able to provide safety to its citizens.
"Millions of citizens continue to live in a state of constant tension and fear, not knowing what to expect next.
"I appeal to all citizens of goodwill to be united in this time of sadness and loss.
"Our solidarity is essential to show the terrorists that we condemn their methods of senseless violence."