The administration-hit Edinburgh club have been banned from signing new players and fined 15 points for breaching insolvency rules.
A positive start to the season that has seen them pick up four points from their first three games has been tempered by a knee injury that has ruled experienced campaigner Ryan Stevenson, 28, out for seven weeks.
With just two other players aged older than the squad average of 22 - goalkeeper Jamie MacDonald and utility man Jamie Hamill - Locke can ill afford to lose any more players from his fresh-faced first team.
And for that reason, anyone collecting petulant cautions and suspensions will be severely punished.
Robinson said: “We can’t afford any injuries right now or suspensions. We’ve been told to cut out stupid things like picking up yellow cards for talking back to the referee.
“We need everyone available with the squad being so small.
“The gaffer had a meeting with us at the start of the season and spelled out that if anyone gets booked for kicking the ball away or talking back to the ref they will be fined.”
Stevenson injured knee ligaments in the 1-0 Edinburgh derby win over Hibernian two weeks ago but could be back in time for the busy festive period.
“We’re missing Ryan right now, he’s a big character for us,” said Robinson, before joking: “He can be like a new signing coming back in when he’s fit again. We can’t sign anyone right now so he can be our new addition in January.”
Robinson missed out on the second half of last season after suffering his own derby knee injury in the goalless Tynecastle draw in January.
Fit again, he has found himself having to act as one of the older heads in Locke’s squad, despite being just 21 himself.
“It’s brilliant being back,” Robinson said. “I had a hard time being out injured. To be out for five and a half months was tough but now to be right back in the thick of it is great.
“I made my debut in 2008, I think - it was so long ago. I’ve seen it all in that time. I’ve worked under three or four managers and now I’m one of the more experienced boys in the team.
“Darren Murray, our youth coach, has told me that a lot of the younger boys will look up to me now and I’ll have to set an example in the dressing room. I look forward to that challenge.
“It’s crazy though that I’m in this situation at 21. It’s a bit surreal. But it’s what I have to handle and so do the other boys. We have to come together as a squad and do what we can.
“Some of the lads in the team are young, the likes of Jason Holt, Jamie Walker and Kevin McHattie. But because they have played so many games you can’t really think of them as kids anymore.
“But we all want to play every week and it this is the way it has to happen, then we will take it.
“There is ability in our changing room and if we can get on a run I’m sure we can pull through.”
Hearts welcome Aberdeen to Tynecastle on Saturday hoping to chip away at another chunk of their points deduction.
They earned a point last week against Partick Thistle when Walker struck two minutes from time to immediately cancel out Aaron Muirhead’s late penalty for the Firhill hosts.
And Robinson says the strong bond forged by the club’s off-field troubles will again be crucial against the Dons.
He said: “Everyone is buzzing after we managed to get off to such a good start. Friday night was crucial. Last season, I don’t think we would have got that goal late on.
“Having lost the penalty so near to the end, heads would have dropped a year ago but there is a lot of team spirit this year and that will help us against Aberdeen.”