Saints take on the reigning Premier League champions at Wembley on Saturday, with a place in the final against Leeds or Chelsea up for grabs.
Hodgson, while admitting that Man City have more quality, feels his Robins side posed many of the same problems Saints will face on the weekend.
The former England boss, who is the oldest manager in the Championship, wished Eckert, the youngest boss, well before the biggest game of his tenure.
Hodgson said: “He is very respectful. He seems like a very nice man. I’m looking forward to having a quick drink with him before we get on the coach.
Southampton manager Tonda Eckert stood alongside Roy Hodgson. (Image: Stuart Martin)
“The club is in a very good state. The thing with the play-offs is that it’s a bit of a lottery. I’m sure they will want to get an automatic promotion place.
“We did a lot tonight with the way we played and kept the ball, which he will be meeting again when he plays Pep [Guardiola, Man City manager].
“They have more quality than we can put on the field, but it’s a great achievement to get there, and it was a great performance against Arsenal.
“Southampton are going to have to do that again, but it will be slightly different. There will be more action in their own goalmouth, I fear.
“Our chances often came on the counter when there was space. You can block spaces, but it means the ball goals into your penalty area.
“Then you don’t want someone like Erling Haaland sniffing around. I was 28 when I started, let’s hope he [Eckert] has a very long career in front of him.”
Saints take on Premier League title-chasers Man City in the FA Cup semi-final at Wembley Stadium from 5.15pm on Saturday, April 25.