The former Dundee player added: “It’s not nice. I’ll tell you that as a player’s perspective. It doesn’t leave you. It haunts you every minute of every day when you’re not winning.
“Getting home, not speaking to anybody, sitting on the couch, not moving, just doing that black screen instead of having the darts or having the football highlights on.
“But, as I said, that is what it comes with playing with Celtic. You need to take that pressure on. You need to get there. You need to show personality and at times within games, we’ve not done that good enough.
“Within the structure, we’ve not done it good enough. But that’s just the kind of rubbish message just now. We need to stick together and keep going.”
It was the second time in a matter of weeks that Celtic had led by one at the break but ended up losing after a similar defeat away to Dundee United.
“Rangers changed their shape and we didn’t react well enough to it,” said McCowan.
“We just aren’t reacting to it as well as we should be. It’s just not good enough.
“I’m probably going to say that at least 20 times in these interviews, but it needs to be better.
“Rangers can’t be coming here and winning 3-1. It’s just not good enough.”