Smith threw two touchdowns, completing 23 of 34 passes for 212 yards with no turnovers, in the Seahawks' 27-13 victory over the New York Giants on Sunday. He should have had a third TD pass if not for a Tyler Lockett drop on a would-be score.
The 32-year-old Seahawks quarterback has been a revelation this season, having spent the past seven years primarily as a back-up, before taking over from Russell Wilson after his trade to the Denver Broncos.
Smith has already this year matched his career-best 13 touchdown passes in a single season from 2014, with nine games remaining.
"He's the real deal, we're seeing it," Carroll told reporters. "There's no mystery or, 'Oh, he's going to run out of gas or something.' It's not like that.
"He knows exactly what he's doing and he shows you week in, week out, throw after throw after throw. There's nothing for us to hold him but in the highest of expectations, really.
"What a thrilling story for the kid. He just hung in there so tough and outlasted it and now he's enjoying all the fun of it. He did great."
Smith has completed 181 of 249 attempts with a 72.7 completion rate for 1,924 yards with three interceptions this season.
The Seattle QB has also rushed for 158 yards with one touchdown, but would not get caught up in the universal praise coming for him as the surprise of he season.
"Man, we just got a win today," Smith said. "We only got a chance to play one game today, and we won it.
"We've got to continue to play hard throughout the season. Every single game is going to be a test. We know that.
"We always talk about each game being a championship opportunity and so we're just going to continue to focus on it day by day, not get caught up in the outside noise - and just do what we do."