Martin had taken Southampton back into the Premier League after beating Leeds United in the Championship play-off final at Wembley in May, but admitted he had been "embarrassed" by his side's lowly top-flight points total before his near-18-month spell in charge came to an abrupt end.
Just as for the 2-1 Carabao Cup quarter-final loss against Liverpool on Wednesday, interim boss Simon Rusk led them from the dugout, with Juric's first game in charge set to be the home game against West Ham on 26 December.
Speaking about his new boss, Ramsdale said: "We met him and, from what came across, he wants to be high pressing, a little more aggressive, hard to beat, crushing spaces and playing in the right areas.
"We probably kicked more today than he would like to, so it's about finding that balance between kicking when we can and letting our boys in attack enjoy themselves."
Juric was constantly chatting tactics with his coaching staff up in the stands, sometimes in Italian, sometimes in English.
Early signs are he will expect his team to press more and applauded one that won a throw-in and was then critical when they were sitting off too much. "Steal the ball," was one call when they were not engaging.
One of the hallmarks of Martin's side was playing out from the back and knocking the ball around defence, but they may adopt a more direct style, with Juric unhappy when the Saints played a number of passes along their backline without getting anywhere.
One thing the new manager did like was a superb run from Tyler Dibling from halfway before he was blocked out by the home defence. The 18-year-old English forward has been one of the few bright sparks for Saints this season and Juric will be hoping to help him progress further.