Qatar has been strongly criticised for its human rights record and the conditions in which thousands of migrant workers have been subjected to as they build the infrastructure needed for the tournament, which kicks off on November 20.
Qatar has also been criticised for its anti-LGBTQ laws.
Southgate said he would continue to speak out about human rights issues before and during the tournament, but in an interview with CNN he said there was no question it should go ahead.
"I've been out to Qatar several times and I've met with lots of the workers out there and they are united in certainly one thing, that's that they want the tournament to happen, and they want that because they love football," he said. "They want the football to come to Qatar."
A report published by The Guardian last year - "categorically" denied by authorities - said 6,500 migrant workers had died in Qatar since it was awarded the World Cup 10 years ago.
Amnesty International published a briefing last month - 'Unfinished Business: what Qatar must do to fulfil promises on migrant workers' rights' - which found that thousands of workers are still being denied wages or having them delayed, being denied rest days, being exposed to unsafe working conditions, facing barriers to changing jobs and in accessing justice.
Amnesty recognised that the 2017 overhaul of Qatar's labour system has led to improvements in conditions for the two million migrant workers in the country but said a failure to fully enforce or implement these changes was undermining progress.
A statement issued last month on behalf of the Supreme Committee, which is responsible for organising the tournament, read: "The advancements in workers' welfare is a legacy we are very proud of, and one that we are already seeing in action.
"We have always believed that the World Cup will be a catalyst to accelerate positive initiatives, leaving a legacy of meaningful and sustainable progress for the country and region."
Southgate said the Football Association would continue to engage with human rights groups to discuss what action can be taken.
"As an FA we've talked to human rights groups about what they would like to see, and we're trying to support those ideas with compensation for families who have lost workers and a worker's rights centre," he said. "So, we're supporting the things we've been asked to support."
England skipper Harry Kane is one of several national captains who plan to participate in the 'OneLove' campaign during the tournament to oppose discrimination.
"In years to come I know I'll look back and think what a life experience and what an amazing thing to have lived through," Southgate said.
"I mean, in the end, the football is everything. It's why we're there. It's what we're there to do."
Asked about England's chances of success in the tournament, Southgate said: "There are some complications with how regular some of our important players are playing.
"There's going to be injuries ahead of the tournament and how badly is that going to affect us? It's pointless looking further ahead, but of course ultimately there's no point us going if we're not trying to win it.
"There's more expectation than when we went to Russia (in 2018).
"But whenever you put an England shirt on, there's always pressure. The incredible highs that you get of leading your country to those great nights are always going to be balanced with difficult times and discomfort, and you've got to lead through that.
"You've got to get your best players on the field in a manner that gets the best out of them. And then, of course, you have to deliver in the tournament. That's where you'll always be judged as an international manager."