Thompson was left raging at Sheffield Arena on Wednesday night, despite seeing his team come back from 2-0 down after 40 minutes against visitors Dundee Stars to win 3-2 after a shoot-out.
But while the two points gained were enough to send the Steelers second in the early misleading Elite League table ahead of Saturday's Challenge Cup home date with Nottingham Panthers, Thompson's main concern is how he can get his side to be competitive against their fiercest rivals.
Having already fired two of his 16 summer recruits last week in the shape of twin brothers Matt and Ryan Rupert - both rejoining ECHL outfit the Indy Fuel two days ago - Thompson said he is not averse to making further changes, although he insisted he needed to get at least one new body in before he could contemplate depleting his existing resources any further.
Part of the reason for his reluctance to wield the axe again just yet is partly down to the upper-body injury being carried by British forward Rob Dowd, a situation expected to keep the 30-year-old GB international out for up to four more weeks.
And having only so far replaced one of the Rupert twins - the experienced Brendan Brooks flying in on Saturday - Thompson feels at least one more body has to land in South Yorkshire before he can look at pulling the trigger.
When asked on Wednesday night whether more changes were in the offing, Thompson replied: "Maybe - because it’s just not happening is it? How many weeks are we going to keep asking this question? All I want us to do is play with a little bit of steel, but that’s not happening. I’m speaking to two players now and I hope and pray that we can get them in for the weekend.
"But we’re a poor hockey club right now and the only way that is going to change … I’ve protected these guys and I’ve took all the heat and all the pressure and I’ve done that for 25 years of my life and I don’t accept that (the performance against Dundee)
"And whether I’m here or whether anyone else is here, there are players here right now that are not worthy to wear the Steelers shirt at this point and it has got to get better."
Thompson is well aware of the growing disquiet among some fans - particularly on social media - while boos rang out in small pockets of the crowd at the end of the second period of the Dundee game. He understands their frustration but is confident he is the man to turn around the team's performances.
"You look at the cvs in our locker room and you look at the cvs in theirs (Dundee's) - and this is not meant in any way to be disrespectful to Dundee because we pay a lot more than them - but, you would have thought the big pay was in their locker room, not ours," added Thompson.
"We can all dress it up as much as we like. I’ll be finger-pointed at like I always am because I signed the guys and rightly so. I can’t hide from that and, if I’m still here, I will be changing them as well.
"Everything I’m telling you here I’ve already said all this in the room, I’ve said it to the players, I’ve said it to their faces. But the fans need to know how I feel about this right now. We’ve just got to move on and start producing."