Rose's goal was his first in the Premier League this season and his first for Tottenham since his stunning winner against Arsenal four years ago.
Sherwood admitted he feared the worst when the 23-year-old pushed Geoff Cameron, saying: "My heart was in my mouth.
"He's the match-winner for us today. I thought he was performing really well and I didn't really want to bring him off but I had to defuse the situation.
"I've never heard a crowd so hyped up. I thought I had to get him off and send him to the dressing room - out of sight, out of mind.
"He's still a young guy, he's still learning his trade. We're smiling because we haven't been reduced to 10 men and he can learn from it.
"It is a positive because we've come away unscathed. We've got a clean sheet and Danny will grow from that.
"He did make the referee make a decision and he shouldn't really be putting himself in that situation. I've told him."