Merseyrail fined me 100 pounds for a 3.75 return journey

I know that I'm technically in the wrong because I did not show a physical ticket - I presented the physical ticket at the onboarding station and lost it on my way to the train.

An appeal is worth my time? I can send them my bank snapshot with the charge from the physical train station purchase.

Is it possible to build a case on this? I'm also a full time student that doesn't receive maintenance loans/cost of living support, so I literally DO NOT have the money. Help.