Stevenson found himself standing in for disgraced skipper Derek Riordan - sent off in the dying seconds of the 2-0 defeat for a reckless lunge at Hearts midfielder Rudi Skacel - for a question and answer session with hospitality guests.
And it was, he admitted, the most uncomfortable experience he'd ever wish to endure.
He said: "They were a lot nicer than I thought they'd be, but it was one of the hardest things I've had to do, facing the fans straight after losing a derby.
"After a performance like that all you want to do is make a quick exit, get home and lock the door. I'd rather have gone straight back out onto the pitch and played the game all over again than have to do that.
"I left for home as soon as I could but I stopped for bread and milk on the way and I could see the disappointment in the faces of the Hibs fans I bumped into.
They didn't say anything but it felt as if there were daggers in your back."
As disappointed as he and his team-mates are, the 22-year-old insisted they had no option but to soldier on in a determined effort to turn around a season which is threatening to totally disintegrate.
An early Europa League exit was followed by an equally quick loss of interest in the Co-Operative Insurance League Cup while league form was just as dreadful, a situation which led to manager John Hughes leaving after only 16 months in charge.
Hughes' successor, Colin Calderwood, has fared no better, losing his first three games as Hibs have slipped to second bottom of the SPL, a mere two goals better off than St Mirren with a miserly eight points from their opening 11 matches.
It's a scenario which has led to many Hibs fans fearing a fight against relegation, a painful experience they endured only 12 years ago and obviously one which no-one wants to go through again.
Today's situation is in stark contrast to just 12 months ago when Hibs could look confidently ahead rather than nervously glancing over their shoulders after a stunning start to the season saw them tipped to split the Old Firm with some even talking of a challenge for the title itself.
Relegated to the bench during the final stretch of Hughes' reign, Stevenson found himself introduced to the action for the first match after the manager's departure, a 2-1 win over Kilmarnock which, like everyone else connected with the club, he had hoped would signal an upturn in fortunes.
Instead, defeats by Aberdeen, Dundee United and, the most humiliating of the lot, the first Edinburgh derby of the season, have seen the first glimpses of sunshine on Leith replaced again by those dark depressive clouds.
Stevenson said: "When we beat Killie you are thinking 'Great, every week can be like this'. The defeat at Aberdeen, though, brought us back down to earth. I thought we were alright against United and deserved something from the game.
"But Sunday was embarrassing. We lost soft goals at the wrong time. After going one down we were doing okay at the start of the second half but then lost another which deflated us at bit.
"We didn't really rise to the challenge and we, as players, have to take the responsibility."
Like everyone else, Stevenson cannot explain why a team which was flying so high a year ago has suddenly crashed with such devastating effect. Some have identified the fact that 16 players, Stevenson included, are out of contract between now and the end of the season but the player insisted that wasn't distracting his focus. He said: "I can only speak on my own behalf but it isn't something I am thinking about at the moment. It's not about contracts but winning games.
"What will happen will happen. If I play well enough then it's up to the gaffer to make the decision. All I can do is keep my head down, play better and show that heart and commitment."
Whatever the reasons, the upshot is a situation entirely of Hibs' making, one which Stevenson insisted can be rectified. "There are ups and downs in football and we are due a few ups. We don't want to be looking at it as a fight against relegation but realistically we need to get a few wins together before we can forget about it, a couple of wins can put you back up the league."
Having said that, Stevenson agreed it was more a case of one step at a time, the immediate need to get that all-important first win under Calderwood and then look to build from there.
However, it doesn't get any easier for the Edinburgh outfit with the daunting prospect of tonight's trip along the M8 to face a Rangers side out in front again as they seek a third successive championship. Accepting that few will see Hibs taking anything from the game. Stevenson said: "We are on a tough run of games with three out of four away from home and we've had a few injuries but we just have to put in a better performance.
"If we can get a draw or even a win it would be great for us. It wouldn't let us forget everything that's happened but it would be a step in the right direction.
"Of course it will be tough, I can't remember the last time Rangers lost at home but Inverness Caley went there the other week and came away with a draw.
"We can almost take the attitude that we have nothing to lose, no-one will be expecting us to do anything so we have to go out there, fight our corner and see what happens."
Hibs' cause isn't helped by the fact they'll go into the match with only Lithuanian hitman Valdas Trakys, who has yet to start an SPL game, as their only recognised striker following Riordan's early bath.
Stevenson, though, insisted it was for others to fill the void left not only by the absence of Riordan but the injured trio of Colin Nish, Darryl Duffy and Merouane Zemmama.
The former Scotland Under-21 star, who has yet to score a first-team goal, said: "It is up to us in midfield to chip in, there's not a lot of goals between us and that's something we have to work on.
"It's been hard for the new gaffer, obviously not the start he wanted, but everyone connected with the club has to pull together. We've been through bad spells in the past and come through them and it is up to us do so again."