Paul Warne's harsh words help Owls-beating Rotherham United tighten their grip on pole position
However, they struggled up to the break at rain-lashed Hillsborough and Warne didn't mince his words as he delivered his half-time team talk.
"Wednesday are a really in-form side who are especially good at home," the manager said. "They had too much for us in the first half.
“We had to change it and I had to tell a few home truths. The lads knew they hadn't performed."
Cheered on by 3,500-plus followers, Rotherham re-established their nine-point advantage over second-placed Wigan Athletic and are 11 points clear of MK Dons in third. They also have a game in hand over the Dons.
Wednesday went into the clash having won five of their last six outings and looking to break into the play-off slots. They had their chances but couldn't take them in the clinical way Rotherham converted theirs.
Ladapo pounced in the 58th minute after a well-worked corner routine and Smith stroked in a quality clincher six minutes from time to give the Millers a sixth straight league victory.
"Overall, it was a similar game to AESSEAL New York Stadium (in August) only reversed," Warne said. "We were the better side at home and lost 2-0. Wednesday were the better side today and we've won 2-0.
"We got a good goal from a set-piece, defended doggedly and rode our luck on numerous occasions. I don't think the best team won, but I'm not complaining.
"We kept a clean sheet and found a way to win. The lads put their bodies on the line and it's a good three points."
Owls boss Darren Moore said; "I look at it today and think ‘Yeah, that’s why Rotherham are league leaders.’
"They’re dogged, they stay in games. They’ve had two shots on target and they’ve scored two goals. They’ve taken the chances when they came and you have to give them credit for that.
“We had three one-on-ones today against the meanest defence in the division. When I look at the chances created, I have to be happy with it."