Josh Windass’s double had seen the Owls leading at the break and the strugglers appeared to be on their way to a welcome three points until Luton hit back in the second period with goals from Kal Naismith, Ryan Tunnicliffe and new striker Elijah Adebayo.
Thompson admitted: “It was probably as well as we’ve played first half.
“We created chances, lots of them, got a great reaction from midweek which is what we wanted, showed a lot of energy, and probably should have been more than two up.
“Luton upped their tempo, but it was a bit of a stop-start beginning to the second half, we couldn’t get into any rhythm, but that’s no excuse, you’ve still got to track runners and deal with balls in the box.
“One of the goals was from a corner which they’ve worked well and two of the goals came when we should have won possession in their half but we didn’t and got punished.
“I always give everyone a well done at half-time when they’ve had a good half, we speak about ‘they’re going to come at us, they’re going to make changes’, they did that and we weren’t able to cope with it.
“You need to do the basics right, that’s what we’ve got to do and we didn’t do that second half.”
Luton chief Nathan Jones was left beaming with pride and said: “To a man in the second half they were outstanding. I don’t think they had a shot on target whereas first they could have had a hundred, literally could have had a hundred.
“It was just such a chalk and cheese performance, the levels went up, the basics went up, every single thing went through the roof and I’m just so happy and proud.”
It had looked like the Owls were going to romp to a simple victory in the first period, as Windass opened the scoring after six minutes, finishing off Calum Paterson’s cross from close range.
He then missed a one-on-one when going through on goalkeeper Simon Sluga, but made amends two minutes before half-time, firing into the top corner.
Luton made three changes at the break and were back in it after 52 minutes through Naismith’s neat finish.
Tunnicliffe made it 2-2 with his first goal of the season, converting Adebayo’s cross after 58, before the Hatters won it with four minutes left, Adebayo rising highest to head home Harry Cornick’s pinpoint delivery.
Luton Town: Sluga, Pearson, Cranie (Rea 46), Potts, Clark, Tunnicliffe; Morrell (Mpanzu 46), Dewsbury-Hall, Naismith, Ince (Cornick 46); Adebayo. Unused substitutes: Shea, Berry, Hylton, Moncur, Collins, Bree.
Sheffield Wednesday: Wildsmith, Urhoghide, Lees, Borner (Dunkley 83), Harris; Hutchinson, Brown, Bannan, Penney (Reach 68), Paterson (Rhodes 68); Windass (Marriott 79). Unused: Palmer, Pelupessy, Hunt, Jackson, Kachunga.
Referee: M Salisbury (Lancashire).