The former Argentina international's 16-month reign at St Mary's came to an end on Tuesday, when he penned a five-year deal to fill the vacancy at Tottenham.
Pochettino's departure has raised questions over the direction of the club and future of a number of Saints' players, such as England internationals Luke Shaw and Adam Lallana.
However, chairman Krueger insists players will only leave on their terms and that the club's recruitment process is already gathering pace.
"We have the highest quality managers in Europe knocking on our door," Krueger said.
"We also have the highest quality available players and their agents knocking on our door. There's a lot of exciting people that want to come here.
"Right now, the focus is on people leaving, but that's normal news broadcast. Behind the scenes there are many people interested in what we're doing here.
"I believe the fact there's so much interest in our manager and our players is also a sign that we're doing the right things here in Southampton.
"Les Reed [Saints' football director] is inundated right now with managers who are interested in taking this club forward and I believe we're in the strongest position that this club has ever been in."
Saints have 20 people working full-time on scouting and recruitment, all of whom are targeted on bringing the best staff and players to the club.
"This same group was involved with finding Mauricio Pochettino, and they were involved out there searching and recruiting profiles which they continue to do because that's their job," Krueger said.
"A club does not invest in 20 recruitment people if it doesn't want to improve or have ambitions to play European football, so we have all of these people employed which is a clear example of what we're trying to do."
Krueger highlighted the importance of Saints moving "swiftly" in appointing a new manager but promised not to rush the situation.
Murat Yakin and Ronald Koeman are the current bookmakers' favourites to take the St Mary's hotseat, while former Swansea manager Michael Laudrup is said to be in the running.
Press Association Sport understands Sunderland will resist any moves for Gus Poyet, while a number of other candidates have been given short prices by the bookies.
So far no outstanding candidates have come to the fore in terms of succeeding Pochettino, but fans' favourite Matthew Le Tissier laughed off suggestions the club will go into meltdown.
"This football club has sold a lot of good talent and people have written us off before," he told Press Association Sport.
"We keep producing players and if you lose a couple, we've got players that can come through and take their places.
"If we do lose a couple, we'll have a lot of money there to go out and spend, so I think, for me, if you appoint a decent manager who is going to use the money wisely, then I don't see any reason why we can't have a similar season to last season.
"We've been doing it for years, back to Alan Shearer's time. I remember people back then saying, 'You've sold Shearer, you're going to get relegated'. I don't go with the whole meltdown, panic thing."
- Sports & Recreation
- Mauricio Pochettino