In his first response to the attacks, Mr Karzai praised the performance of the Afghan security forces.
He said they had proved themselves capable of defending their country.
Officials say 51 people died in the fighting in Kabul and elsewhere: four civilians, 11 members of the security forces and 36 insurgents.
“The terrorists’ infiltration in Kabul and other provinces is an intelligence failure for us and especially for Nato and should be seriously investigated,” Mr Karzai said.
The Taliban say they carried out the raids as part of a co-ordinated “spring offensive”. The group usually ramps up its attacks on Nato and government forces in spring, after a relative lull over the winter, when snows hamper the fighters’ movements.
The attackers used a construction site in central Kabul as a base the US ambassador to Kabul, Ryan Crocker, said he believed the Taliban would not have had the ability to carry out the attacks.
He told CNN he believed they were the work of the Haqqani network, a Pakistan-based militant group allied to the Taliban.
Mr Karzai’s office said four civilians had died in the fighting. Earlier, Afghan Interior Minister Besmillah Mohammadi said that about 65 people – including 25 civilians – had been injured.
President Karzai paid tribute to the “bravery and sacrifice of the security forces who quickly and timely reacted to contain the terrorists”, AFP news agency reports.
“They were on scene immediately, well-led and well-coordinated. They integrated their efforts, helped protect their fellow citizens and largely kept the insurgents contained.”
While the Taliban have said they carried out the attacks, analysts say they bear the hallmarks of the Haqqani network