Christian Walton (groin), Kalvin Phillips (calf), Wes Burns (knee), Chiedozie Ogbene (Achilles), Julio Enciso (knee), Omari Hutchinson (knee), Sammie Szmodics (ankle) and Conor Chaplin (knee) were all unavailable for Monday night's FA Cup exit at Nottingham Forest.
On top of that, defensive duo Axel Tuanzebe (hamstring) and Cameron Burgess (calf) were both forced off at half-time at The City Ground.
Asked for a fitness update, McKenna said: "It's a long story, to be fair! We're still in the process of assessing some.
"In terms of those who went off the pitch, Axel (Tuanzebe) won't be available for this weekend and Cameron Burgess (groin) is still be assessed.
"We have or two who may be able to rejoin the squad who weren't involved on Monday night, and we'll have one or two who were there on Monday night who won't be available. And we've got a few who will be assessed tomorrow.
"It's certainly a bit of a tricky period for us at the moment. We're trying to make the right decisions and get a competitive squad available for Saturday."
On Tuanzebe, who has already missed periods of this season with thumb and hamstring injuries, McKenna said: "I don't think it's as bad as the last time. He has a small muscle injury and he also needs an operation on his thumb from the injury before. So he's going to have an operation in the next couple of days on that and that will take a period of recovery. He won't be available this weekend and we'll make assessments from there."
Asked who might be available again, the Blues boss said: "Julio (Enciso) and Omari (Hutchinson) are not too far away from the squad. There's going to be a real decision as to whether there's any involvement for them this weekend.
"Conor Chaplin is still working by himself. Sam Szmodics has gone for an ankle operation, unfortunately. So he's going to be out for an extended period of time. He originally suffered the injury in a tackle in the Fulham game, then had a recurrence of it in the Coventry game, then he had a recurrence of it after the Man United game. I don't know the exact timescale, but it's going to be a good number of weeks and if we see him again this season it will be in the last couple of fixtures.
"Kalvin (Phillips) trained today. He's in a better place. Again, we'll make a judgement.
"Christian (Walton) is going to be in the squad this weekend hopefully. Aro (Muric) has had an injection in his shoulder, he's done really well to be available for the team to be honest over the last couple of weeks, but it's got to the point where it needed to be addressed.
"Honestly, it's a real mixed bag. We've got some working on the grass with rehabilitation coaches, some who are just trying to reintegrate with the team and Sammie joins the list of players we're not going to see too much of this season."
Burns and Ogbene were deregistered from the squad last month having both suffered long-term injuries.