Southampton boss Koeman has kept the Saints competing for a European spot all campaign and the Sky Sports punditry duo both believe he has done a brilliant job.
Carragher says that the work that Koeman has done on Southampton's defence deserves to be praised, with the south coast outfit boasting the second best defence in the entire league.
"He made a great start and you’ve just got to go back to the start of the season to see the players that they lost, the players that came in and all the talk of relegation," he said.
"They were good defensively under Mauricio Pochettino but you can see Southampton are a well-coached team and it’s down to the work Koeman has done. They are just behind Chelsea with their defensive record and that shows the work of Koeman on the training ground."
Neville, meanwhile, was keen to focus on Southampton's attacking quality, which was on full display in their last fixture.
Southampton beat Aston Villa 6-1 last weekend and it is not the first heavy victory they have recorded this season - with an 8-0 triumph over Sunderland also impressive.
Neville feels that these results were due to the work that Southampton put in on the training ground and he says he enjoys watching the trio of attackers Koeman uses work in tandem.
"I've gone for Koeman as well but for different reasons," he said.
"If you think about the end of last season, Southampton lost their front three. They lost Jay Rodriguez to injury and Rickie Lambert and Adam Lallana to Liverpool but whatever front three he has played this season, they’ve got attacking organisation. Attacking organisation is something I like as much as defensive organisation and with Southampton, you get it."
Southampton are currently seventh in the Premier League table and they can still make it into Europe, if results go their way on the final day of the campaign.