David Smith, whose 14-year-old daughter Hannah was found dead in her bedroom earlier this month, described Ask.fm's new measures as "a good thing".
But he said that in making changes, the site had "admitted that their website was dangerous for teenagers."
"It's now time for the Government to step up and start regulating these websites so that a 45-year-old lorry driver doesn't have to do it, because I haven't got time to do it any more," he added.
"It's not just Ask.fm, it's the whole internet. The Government actually do need step up and start regulating this internet to make the internet a safer place."