Bill Belichick stood, as he always does after Patriots home games, stone-faced at the interview-room podium late Saturday wearing a pair of jeans and an expression that told you he’d rather be locked in a closet with his ex-wife.

His Patriots had just dispatched the flawed Texans, 34-16, in an AFC divisional playoff game to advance to their sixth consecutive AFC Championship game, a remarkable accomplishment that should have had the venerable coach euphoric.

Yet there was angst on the face of Belichick. Because there always is.

But this time, that familiar look of disdain was fake, because the perfect night had just unfolded for Belichick, who had to be beaming on the interior of that gruff exterior.

Belichick didn’t just win his NFL-record 24th postseason game, he won the head-coach lottery: His team survived and advanced and did so while displaying so many flaws, it hand-delivered fodder for him to use like a horsewhip with his players as they prepare for next Sunday’s AFC title game against the Steelers.

He got more teaching moments than he could possibly have asked for in the win Saturday night. Interspersed with the good things the Patriots did — among them three touchdowns by running back Dion Lewis, including a 98-yard kickoff return, and three interceptions by three former Rutgers defensive backs — were two Tom Brady interceptions, a fumbled kickoff return by Lewis and a game-turning personal foul by defensive back Eric Rowe.

All were classic teaching moments, and coaches crave teaching moments the way kids crave candy bars.

In short, what Belichick got along with the victory was a total elimination of any potential complacency leading into this weekend’s conference title game.

“We’ve just got to learn from it,’’ Brady said of the less-than-impressive win.

“We made plays when we had to, but if we want to keep winning and move on, we can’t play like that,’’ Patriots leading receiver Julian Edelman said.

“We worked hard to get here and we’ve still got a lot of work to do,’’ said Lewis, who served as the perfect microcosm of New England’s imperfect night with his three-TD brilliance tarnished by his lost fumble. “We still haven’t played our best football.’’

Belichick lamented the “mistakes we had — we had penalties, we had dropped balls, we threw the ball right to them, we fumbled it,’’ adding, “Give [the Texans] credit, but we’ve got to do better than that. We’re going to play against another good defense this week.’’

When a local reporter attempted to lighten the mood in the room after an 18-point victory somehow felt like a loss and asked Belichick to reflect on his team becoming the first to advance to a sixth consecutive conference championship game, the curmudgeonly Patriots coach would have no part of it.

The game had been over for only minutes and he already was coaching his team for its next task. The teaching moments, after all, were low-hanging fruit and Belichick hungrily plucked away.

“Well, it’s great to be playing at this time of year,’’ he began. “You’re one of four teams that’s left after the weekend. But … I don’t really care about the other five years right now, or however many years it’s been. The only thing that matters is this year, this team, and what we have an opportunity to do, what we need to do to move on to play again.

“We can talk about all of that other stuff some other time. For right now, it’s just this team and getting to the AFC Championship game and playing our best game next weekend. That’s what we’re going to need to do. We’re going to need to play our best game, better than we played tonight.’’