Speaking exclusively to the BBC's Laura Kuenssberg, she said she understood concerns over immigration but leaving the EU was not a "silver bullet".
Mrs May, who backs Remain, denied she had "been quiet" during the campaign.
She listed the economy and jobs, security, and Britain's "place in the world" as reasons to stay in the EU.
In other referendum news:
Speaking on BBC Radio 4's Today programme, Chancellor George Osborne ruled out any further immediate changes to freedom of movement rules, amid speculation the government could offer further concessions ahead of next Thursday's EU referendum.
Mrs May has previously suggested reform of the free movement rules, saying in April the UK needed to be "smarter" about trying to change them in the future.
She told the BBC's political editor: "There are some changes coming up in free movement rules, to make it easier for us to deal with illegal immigrants and I think again as I've said that we should look at further reform in the future.
"But when we look at the question of membership I understand people have concerns over immigration, but this is about our economy, our security it's about our future place in the world and I  think it's important that people look at all these issues."
She added:  "What I've learned over six years is there's no single answer, silver bullet, there's no one thing you can do that can suddenly deal with all the problems and concerns over immigration and that includes leaving the EU, that's not the single answer to this."
Explaining her reasons for joining the Remain campaign, she said there were "plenty of voices suggesting what I should do on this, quite a lot of voices suggesting I go down the Leave route"  - but she had come to her own judgment by looking at "the facts" and "used my own experience as home secretary and what I've seen over the last six years and I'm in no doubt that we should Remain".
She added: "When I put that all together and I think about the potential risks to jobs, the uncertainties for our economy if we are to leave the EU, and I think about security, the discussions I've had within the EU, I do believe we are more secure in the EU, and this issue of our place in the worldâ€¦I believe we should stand up and stand tall and lead in Europe"
On security, she said "as home secretary that's a key issue for me and I genuinely believe that everything I've seen over the last six years that we would be more secure and safer inside the EU".
Mrs May did not rule out standing in any future Conservative leadership race but maintained there was "no vacancy" at the moment and she hoped David Cameron would remain as PM until 2020.
She said she thought Mr Cameron would remain in place whatever the result of the referendum as he had been elected last year and "we need to ensure we carry on with that job after the referendum".
She said it was understandable that other Conservatives "who've held very strongly-held views for a long time on this issue" would campaign "very passionately" to leave the EU, but said that party unity would return after the referendum. She said it was a  "genuine desire of most people in the party that we do come back together again".
Home Secretary Theresa May has said the government "should look at further reform" of free movement of people, if the UK stays in the EU.