Lady Thatcher says Britain must stand shoulder to shoulder with the US in the fight against terrorism.
Lady Thatcher said the attack on the US was 'an attack upon us all'
The ex-Conservative prime minister, in Washington to commemorate 9/11, warned: "We must not falter. We must not fail."
She spoke as current Tory leader David Cameron called anti-Americanism "intellectual and moral surrender".
But Mr Cameron also called for greater "humility and patience" in foreign policy, describing himself a liberal conservative, not a neo-conservative.
Baroness Thatcher's comments came in a statement from the White House where she accompanied members of the US Cabinet to take part in a solemn ceremony to mark the fifth anniversary of the attack on the Twin Towers in New York.
She said: "I am honoured to be here in Washington to join with the people of America as we are marking the anniversary of that terrible tragedy five years ago.
"These acts of barbarism brought suffering to thousands of families, both in this country and elsewhere.
"Indeed in Britain, many similar families who suffered loss will be sharing this moment.
"For this heinous attack upon America was an attack upon us all.
"With America, Britain stands in the front line against Islamist fanatics who hate our beliefs, our liberties and our citizens. We must not falter. We must not fail.
"Today, we are here to remember to pray for the dead and to share their loved one's grieving.
"But we also need to renew our resolve that, however bitter or lengthy the struggle, this evil shall not prevail."
Staunch US supporter
Lady Thatcher, joined in the ceremony - at the invitation of US Vice President Dick Cheney - at 0846 Washington time (1246 GMT) - when the first plane struck the North Tower.
Following the White House gathering, she was due to attend another commemoration at the State Department, where she was set to meet US Secretary of State Condoleezza Rice.
Not long after the ceremonies, Mr Cameron used his first major foreign policy speech to distance himself from US President Bush, while declaring himself a staunch supporter of America.
Speaking at the British American Project's annual JP Morgan lecture, he argued that US-British foreign policy had accepted an "unrealistic and simplistic" view of the world.
"On any reasonable measure, the international security challenges are greater today than five years ago," he said.
But he warned: "We must recognise something else - that our attempts to meet these challenges have had an unintended and deeply worrying consequence. They have fanned the flames of anti-Americanism."
Mr Cameron said he found these sentiments "troubling" and an "intellectual and moral surrender", before describing his party as "instinctive friends of America and passionate supporters of the Atlantic Alliance".
The British American Project works to strengthen the relationship between the UK and US