In November residents found that the council website was inaccessible for extended periods, often at weekends.
The website experienced a distributed denial of service (DDOS) attack where the council's servers were hammered with repeated requests, meaning legitimate visitors couldn't access the site.
Michael Scorer, strategic director of housing and modernisation, told councillors on Monday that the council had experienced a "seriously big attack".
"There is is the possibility that they were from foreign governments," Mr Scorer told the overview and scrutiny committee.
Mr Scorer said that the authority believed that it was no coincidence that the attacks took place at weekends, when more residents are trying to make transactions on the council website and fewer staff were available to deal with technical problems.
Cllr Stephanie Cryan, cabinet member for housing management and modernisation, assured the committee that no council systems had been compromised and that steps had been taken to reduce the risk of a similar attack succeeding in the future.
The committee also heard that software updates carried out in the wake of the attack had broken some of the older programs used by the council, so it had taken some weeks till a full service was restored to residents.