Dexter Blackstock's 24th-minute shot struck Darren Purse on the back as he tried to block it but Wednesday's captain was penalised for handball.
Irvine argued: "I thought we deserved to get something out of the game. There was only one person in the ground who thought it was a penalty because the shot clearly struck Darren Purse on the back."
And Davies admitted: "The penalty was a soft one and if I was their manager Alan Irvine I would have been very disappointed by it."
Blackstock sent Wednesday goalkeeper Lee Grant the wrong way from the spot but Forest did not build on their good fortune and the Owls more than held their own and deservedly equalised in the 74th minute.
Substitute Etienne Esajas fired a shot across goal and Luke Varney was left unmarked following a ricochet to shoot past Forest goalkeeper Lee Camp. But five minutes later Forest were in front for a second time when Chris Cohen's free-kick was not dealt with by the Wednesday defence and when the ball wriggled away from Grant, Blackstock gleefully swept in his second goal.
It was rough justice on Wednesday and manager Irvine.
"The penalty knocked us out of our stride for 10 or 15 minutes," he added, "but we talked about a few things at half-time and were in the ascendancy for the second half. I thought we might actually go on and win it because we were on the front foot when we scored the equaliser.
"But when you put into context how good a side Forest are, we can take a lot of heart from the performance. If we perform like that in our other games we will win more than we lose."
Forest, maybe carrying a hangover from their defeat by Derby, were not their usual fluent selves in the early stages but got the big break of the debatable penalty award.
They were ultimately made to sweat during five minutes of stoppage time but held on.
To add to Wednesday's woes, Davies revealed he was about to substitute Blackstock just before he fired the winning goal.
Davies said: "Yes, we were going to make a substitution. Sometimes it works out for you and sometimes it doesn't."
Nottingham Forest: Camp, Gunter, Morgan, Wilson, Perch, Tyson (Anderson 65), McKenna, Moussi, Cohen, Earnshaw (Adebola 69), Blackstock (McGoldrick 83). Unused substitutes: Smith, Chambers, McGugan, Majewski.
Sheffield Wednesday: Grant, Simek, Purse, Beevers, Spurr, Soares (Clarke 67), Potter, O'Connor, Gray (Esajas 67), Tudgay, Varney. Unused substitutes: Jameson, Hinds, McAllister, Lekaj, Boden.
Referee: Trevor Kettle (Rutland).
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