The Dutchman has guided the Saints up to second place in the Premier League table since he joined the club from Feyenoord in the summer.
Beattie believes that Koeman's "astute" management style and some impressive work in the transfer window has given the team a new lease of life after seeing a number of key players leave at the start of the campaign.
"Ronald Koeman has come in and he looks very astute, very calm and calculated," he told Sky Sports News. "His management skills are looking pretty good with the players he has brought in like Graziano Pelle who couldn't really score early on but now has started to get goals.
"They have a new chairman in Ralph Krueger and the players they have brought in have hit the ground running and that is testament to themselves and management."
Southampton continue their League Cup campaign on Wednesday when they travel to Stoke City in the fourth round.