Vichai Srivaddhanaprabha was killed when his helicopter crashed into a car park outside the King Power Stadium following the Premier League match with West Ham two weeks ago - a game Southgate had attended.
"Leicester have been through an incredible couple of weeks," said Southgate, speaking at Wembley this week.
"It's important to give them space to take all of that in. My impression is that they feel it's important to get on with football as well. I think the tributes have been wonderful.
"I was there on that day. You actually left the ground saying, 'What a lovely family football club.' To think that 20 minutes later they were thrown into what has been the last couple of weeks is incredible. Incredibly sad for the families of those involved directly in the accident and incredibly sad for Leicester City and the people there.
"It's remarkable the way they have dealt with everything and it's been very emotional to watch, especially before the game last week. The huddle with all of the staff and the players, because you know having been in teams and football clubs what that will have meant to everybody there. I think they've found a really good balance of paying their respects and recognising that life has to go on and you carry on professionally."
"The first thing is to allow the club space," he added.
"There are some people at the club whom I know very well, both on the playing side and behind the scenes. I always think that the process of grieving and remembering is a very personal one. You are there to support if needed, but equally you have to give people the time and space to do those things. Saturday is another hugely emotionally occasion.
"After that there is a chance to speak to one or two of them, particularly people I know pretty well there, as much as anything to comment on how brilliantly I think they have dealt with it all.
"Susan Whelan, the chief executive and Jon Rudkin, the director of football, both of whom I know really well, Andrew Neville (director of football operations), who has been with us to a couple of our recent England games as an ambassador. They will have been at the forefront of how the club has dealt with all of those things. I think they have done it brilliantly.
"The whole community there in Leicester seems to have appreciated that and come together. It's a reminder that a football club is a focal point for the community around many things. I think the owner captured that in the way he ran the club. They've managed to do that, it seems, from the outset and over the past couple of weeks", he added.