Owen Farrell landed a penalty via both posts with the last kick of the game to earn Saracens the points in a pulsating finish to a second half in which the lead changed hands five times.
Nick Short scored the visitors' only try, against efforts from Nick Abendanon and Carl Fearns for Bath, but Farrell's 23 points settled the match in Sarries' favour, 28-26.
"We've got the season up and running, which is important," said McCall.
"It was a disappointing start last weekend against Wasps. Bath is a very difficult place to come - but everyone in the club has worked hard this week."
McCall was particularly pleased that his players appear to have retained the knack of winning away from home.
"We won eight or nine of our Premiership away games last year, which proves that our players don't pick and choose when they get up for games," he said. "They just get up for it every week and they prepare well, whether it's at Twickenham or wherever."
He also paid tribute to skipper Steve Borthwick's contribution in ensuring that Saracens were in a position to take the spoils in the last seconds of the game.
"Steve had a great game," said McCall. "He was instrumental in stopping their maul, which is one of their main weapons. He's an exceptional player for us."
Bath coach Brad Davis said he could not really fault his side's quality of performance or the spirit they showed.
"We went toe-to-toe with arguably the best team in the Premiership," he said. "At the same time we have to temper that with feeling bitterly disappointed that we couldn't control the match at the end and allowed the opposition into our half and to win that penalty.
"But what was pleasing from our perspective was that we showed a level of performance and a level of intensity that is up there with the best. In fact, but for a dubious 50-50 call at the end I thought we shaded it.
"You are never going to dominate a side like Saracens for 80 minutes. We had our moments and they had their moments and that was reflected in the scoreline - just two points at the end of it."
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