An Indian intelligence warning from the beginning of the month about planned attacks was not properly shared by the authorities, parliament heard.
Meanwhile, the pregnant wife of a Sri Lanka bomber detonated a suicide vest when police raided the family home in the wake of the terror attacks, killing her own children.
Her husband was one of two brothers at the centre of the plot in Colombo.
As well as her unborn child and two children, three police officers also died.
President Maithripala Sirisena has moved to sack the defence secretary and inspector general of police.
Eight of the nine attackers have been identified as Sri Lankan citizens.
The government is investigating whether the Islamic State (IS) group was involved in the attacks which targeted churches and high-end hotels.
Police are still searching for the leader of a local Islamist group, Zahran Hashim, who was among eight people in a photograph released by IS. It is not clear whether he was among the nine suicide bombers.
It has emerged that one of the attackers once studied in the UK and Australia before returning to Sri Lanka.
"We have to take responsibility because unfortunately if the sharing of the intelligence information had been given to the right people, I think that at least this could have been avoided or even minimised," said Deputy Defence Minister Ruwan Wijewardene.
Lakshman Kiriella, the leader of parliament, said senior officials had deliberately withheld intelligence about possible attacks. "Some top intelligence officials hid the intelligence information purposefully," he told MPs. "Information was there but the top brass security officials did not take appropriate actions."
He said the Indian tip-off had been received on 4 April but, Reuters news agency says, both the president and Prime Minister Ranil Wickremesinghe reportedly did not receive it.
President Sirisena replaced Defence Secretary Hemasiri Fernando and took steps to sack the Inspector General of Police, Pujith Jayasundara.
British connection to one attacker
A UK government official confirmed the name of the bomber who had visited the UK as Abdul Latif Jamil Mohammed. He visited south-east England in 2006-2007 to study but did not complete a full university degree.
Mr Wijewardene said the attacker had gone on to do "his postgraduate in Australia before coming back to settle in Sri Lanka".
He added that most of the attackers had been "well educated and come from... middle or upper middle class" families. "They are financially quite independent and their families are quite stable financially," he said.
Two of the bombers are reportedly brothers and the sons of a wealthy Colombo spice trader. They detonated their explosives at the Shangri-La and the Cinnamon Grand hotels, police sources told the AFP news agency.
Sri Lanka's government has blamed the blasts on local Islamist group National Thowheed Jamath (NTJ) but Mr Wickremesinghe said the attacks "could not have been done just locally".
NTJ has no history of large-scale attacks but came to prominence last year when it was blamed for damaging Buddhist statues. The group has not said it carried out Sunday's bombings.
IS said online that it had "targeted nationals of the crusader alliance [anti-IS US-led coalition] and Christians in Sri Lanka".
It provided no evidence for the claim but shared an image on social media of eight suspected attackers.
Security forces detain around 60 people
Police have now detained around 60 suspects in connection with the attack. A state of emergency remains in effect to prevent further attacks.
The nearly simultaneous attacks targeted three churches packed for Easter services and three major hotels in the capital, Colombo. An attack on a fourth hotel on Sunday was foiled, Mr Wickremesinghe said. He also warned that further militants and explosives could still be "out there" following the attack.
One of the targeted hotels, the Kingsbury, has now reopened.
The country remains tense with police still looking for suspects and possible further explosives.
The first mass funeral was held on Tuesday, as Sri Lanka marked an official day of mourning for the victims.
Most of those who died were Sri Lankan nationals, including scores of Christians attending Easter Sunday church services. Some 38 foreign nationals were among the dead, with another 14 unaccounted for. The death toll includes at least eight British citizens and at least 11 Indian nationals.
A mass funeral for about 30 victims took place at St Sebastian's church in Negombo, north of Colombo, which was one of the places targeted in Sunday's blasts.
- BBC / ABC