Hibs have only suffered consecutive defeats on two occasions this season, both times limited to two matches. Their most recent loss, a 3-1 home defeat by St Johnstone that sparked an angry response from manager Pat Fenlon, was followed by frank talks.
And Hibs would have made it two away wins in a row in their subsequent games had it not been for Johnny Russell's late controversial penalty at Tannadice on Sunday.
Fenlon has added a steel on the park and Stevenson hinted an ever-present determination to avoid defeat has also played a part in turning Hibs from Clydesdale Bank Premier League relegation candidates to European hopefuls.
Stevenson, who is set to start against Killie at Easter Road, said: "We got off to a flyer at the start of the season and had a dip in form. In previous seasons the dips in form have maybe been about 15-20 games whereas this season it is maybe five games, which is not great but it's a lot better than it has been.
"This year when we have been beaten, it shows a lot in the changing room and in training the next week how much it is hurting. Maybe in previous years it has not been like that.
"Especially after the St Johnstone game at home, we know we didn't play well. It was probably the poorest performance of the season. We had a chat the next day in training and got a lot of things out in the open. From there we have kicked on.
"It's a lot easier place to be when you are winning games and playing well."
The 25-year-old has been playing at right-back in recent games, with Tim Clancy still missing with a hamstring problem.
"I have been enjoying it," he said. "It helps when the team is winning and playing well. The St Mirren and Dundee United games are probably the best we have been playing for a while so that always helps."