Flitcroft's men were in firm control and by far the better team until they switched off, allowing Matty Fryatt to score and deny them the three points.
Wednesday, whose winless start to the Sky Bet Championship campaign has extended to 12 games, were woefully off the pace for the opening hour and looked on course for a defeat after Marcus Pedersen scored a fine opener in the 16th minute, smashing home an 18-yard volley.
But on-loan striker Fryatt, who is due to return to parent club Hull, signed off with a superb strike of his own to give the Owls a 1-1 draw and share of the spoils.
"I was disappointed we didn't lock the pitch down for their goal, we left it too open," Flitcroft said.
"So we have to do better and defend better to keep a clean sheet and win games.
"We are growing into the season, I am pleased we are getting better and finding some momentum.
"It's about grinding in and digging results but having the bigger picture to develop a team.
"We did the game plan and it completely worked, the moment we have not focused allowed Sheffield Wednesday to get in.
"I was desperate for a clean sheet and it's disappointing - the quality of Pedersen's goal should win the football match."