The team have recorded just one victory in seven league outings and languish in 10th position after Saturday's 3-0 drubbing by Kilmarnock.
Financial problems have led to the sale of leading players such as David Templeton, Ian Black, Ryan McGowan and Andy Driver and, with injury problems biting, McGlynn has been forced to blood a team full of teenage tyros.
Speaking ahead of the visit of Inverness Caledonian Thistle, a side they beat on penalties to reach the Scottish Communities League Cup final, McGlynn asked fans to be realistic.
"Anyone who feels they've paid their money and want to vent their anger are entitled to do that. That goes with the territory. But if you're realistic and take everything on board that's happened here and where we're going – trying to bring younger players through and get them to gain experience to handle these situations – it is a learning curve based on the future.
"Some will still be critical of me and others will perhaps understand the situation. Football revolves around opinions. Expectations are still incredibly high at the club. There has to be a wee bit of realism at what's actually going on. I think a lot of people do and it will be a minority who don't want to understand the situation.
"It's not rocket science. No club would be able to compete at the same level losing that amount of players. Players who are inexperienced at this level will become unstuck in situations like last Saturday."
McGlynn, who was the club's youth coach before taking the Raith Rovers job in 2006, added: "We've lost our captain, Marius Zaliukas, and Danny Grainger through injury, we've not had Jamie Hamill. We've lost David Templeton, Ryan McGowan and now Andy Driver.
"Who was Hearts top scorer last season? Rudi Skacel. Who was second top scorer? Andy Webster with four goals. Andy's not scored his four goals this season. And we're missing Skacel's (18) goals. We've not got Ian Black to produce that ball or Stephen Elliott or Craig Beattie or Suso Santana.
"We're 90 minutes away from giving the fans the success they want in an incredibly difficult season. It's unbelievably difficult. Yet we could possibly win back-to-back cups and it's 50 years since Hearts won the League Cup."