Saints shipped five goals to Tottenham at Wembley on Boxing Day, but responded with a spirited display and looked just as likely to break the deadlock as hosts Manchester United.
McCarthy was handed a first Premier League start for the club by Mauricio Pellegrino, and rewarded his manager with a clean sheet in the goalless draw.
“It's obviously the perfect start for me," said the goalkeeper. “But the main thing is we got a point and a clean sheet away from home.
“We knew it was going to be a tough game, but hopefully it's a turning point for us.
“The fans travelled to Wembley and they were disappointed, so we knew we had to show a reaction in tonight's game.
“I think they'll see that we've done that. We're happy with the point – we would've liked three points, but we'll take the point away from home.
“The team as a whole was excellent in their defending and going forward as well."