Schneider is unbeaten in the Bundesliga since taking over from Bruno Labbadia earlier in the season, with Bobic insisting that the time was right for a change.
"Bruno is a very good coach," he told Bundesliga.com. "We've mastered many crises together, that was never up for discussion, but there was a moment towards the end of pre-season when the contact between the coach and his team disappeared.
"The results speak for themselves. We're heading in the right direction with a dominance we'd not been able to show in previous weeks."
Schneider has lifted Stuttgart to eighth in the league table.