The Ukip leader had earlier described the ban as "ludicrous" and claimed that it failed to cut gun crime.
Marjorie Davies, who was chairwoman of Dunblane Community Council at the time of the shooting, said Mr Farage's comments were "insensitive and will bring up a lot of bad memories for parents and locals".
She added: "The ban clearly works as there has thankfully never been a repeat of Dunblane in the UK. When you look at somewhere like America it feels like every few months there has been a shooting."
Ann Pearston, who founded the Snowdrop campaign, which fought for the handgun ban, said: "Nothing has changed to warrant a watering down of the legislation. So far it has stood the test of time. There has been nothing like Dunblane since."
Scottish politicians also criticised his remarks.
Keith Brown, the SNP MSP for Clackmannanshire and Dunblane, said: "These comments are truly appalling and deeply offensive to the people of Dunblane.
"Strong gun control laws are essential in helping to ensure that tragedies like the Dunblane massacre never happen again."
Scottish Conservative justice spokeswoman Margaret Mitchell said: "For Nigel Farage to link such ill-advised comments with this tragic event is completely inappropriate."
Thomas Hamilton killed 16 pupils, their teacher and himself in 1996.
Following the tragedy John Major made ownership of most handguns illegal. Tony Blair changed it to cover all handguns, including the pistols used at the Olympics.
Mr Farage told a radio show: "I think proper gun licensing is something we've done in this country responsibly and well for a long time, and I think the knee-jerk legislation Blair brought in that meant that the British Olympic pistol team have to go to France to even practice, was just crackers."