Irish boss Fenlon has faced a backlash from supporters in the days since last Sunday's 1-0 Edinburgh derby defeat to administration-hit Hearts.
The defeat to the financially stricken Jambos was the final straw for many fans after the Leith side lost their first three games of the season - including the mortifying 7-0 home reverse to Malmo in the Europa League qualifiers.
An online survey carried out by popular supporters forum Hibs.net illustrated the depth of feeling amongst the Easter Road faithful, with around 93 per cent of the near 600 respondents calling for a change of boss following that Tynecastle defeat.
But Roberson claims it is the players who must do more to improve results.
He told Press Association Sport: "We can obviously understand the fans' frustration because results have not been good enough. They turned out in great numbers for the European game and it ended up being more a punishment than a reward for them.
"But we've got to be patient. I know it's easy for me to sit here and ask for patience from the fans when they are paying money to come watch what they are watching sometimes, but we as players have just got to be as positive as we can and try to turn it around because it only us who can do it."
While the club's first two Scottish Premiership fixtures with Motherwell and Gary Locke's Gorgie men have been lost to single-goal defeats, it is the 9-0 aggregate defeat to Malmo that has really shaken confidence in Fenlon's leadership skills.
But Robertson insists the Edinburgh men could take on some of the world's top sides and never face another hiding like the one dispatched by the Swedes.
"The reaction has been a bit knee-jerk," he said. "It's only two games into the league season and, okay they have both been defeats, but we have not been outplayed or outfought.
"It has come down to fine margins and we haven't taken our chances while our opponents have. We need to learn to be more clinical because we have created chances. If we had taken them, we could be here talking about us going on a little run, rather than the results we've had.
"The Malmo result has exacerbated things. Okay, no-one should be getting beat 9-0 on aggregate. It doesn't matter who it is you are playing. I wouldn't expect to get beat by that score even if it was Manchester United we were playing."
Former Dundee United midfielder Robertson will face his old side at Easter Road on Saturday hoping to regain the type of form he showed during his Tannadice days.
He won the first of two Scotland caps earned while a United player against an Argentine side managed by Diego Maradona in November 2008 but has not given up hope of returning to the international stage.
And after being forced to watch Wednesday's breathless 3-2 friendly encounter with England at Wembley from his sofa, the 28-year-old admits he would have swapped both his previous run-outs in Dark Blue just to have tasted the action against the Auld Enemy.
He said: "I had a bit of bad luck with injuries after making my debut. It was only a couple of months later that I picked up an injury and never played again for 18 months. Then I had a dip in form and a few other things happened which meant I never kicked on from there.
"I have two caps but I won't say I'll never win another. However, the only way I'll do that is by replicating the form I've shown in the past. My debut was against Argentine and that was a big game because Diego Maradona was their boss but the England match was something else entirely.
"The game on Wednesday was a great game to watch and must have been incredible to have been a part of. I'd have given up the two caps I've won so far to have run out at Wembley."