After 105 days without a game due to football's shutdown, Town produced a laboured, low-quality performance in a flat 2-0 home reverse to the Latics, with Hodkingson revealing on a podcast that he was 'shellshocked' by the level of mediocrity in the display.
On the criticism, Cowley, fully aware of the need for his side to produce the right response in Sunday's game at Nottingham Forest in front of the TV cameras, said: "I don't go on social media after we lose. Sometimes, I go on after we win.
"But going on after we lose is a dangerous place for football managers.
"Listen, I can imagine what people were saying. I get we were criticised. I think it was fair.
"We didn't play to the levels we wanted to play to and with anywhere near enough speed or dynamism and weren't positive enough in our play.
"We did not play with enough aggression at the top of the pitch in terms of our penetration in our runs.
"We have to accept this. First and foremost, we are critical of ourselves and ultimately, I will always look at myself first.
"But then it is my responsibility and job to look at every else around me as well. I think the players enjoy me looking into their eye and telling them the truth. We all need that from time to time.
"We accept the criticism. When we have had bad days before, we have always responded and we have worked hard this week to try and find the right response on Sunday."