Ryanair reschedule flight resulting in missed connection flight

Hi all and happy new year.
I booked 2 return flights with Ryanair shannon to London
then london to Rome and returning Visa Versa 4 days later.
Ryanair have re-scheduled the London to Rome flight resulting in us not being able to make the London to Shannon flight.They have offered us an earlier return flight from Rome which technically would allow us in their eyes to make the London to Shannon flight home,however realistically for all sorts of reasons we would not make it.I have accepted a refund for the Rome flight but they will not refund the Shannon flight as they say connecting flights are not their problem.The long and the short is they have 200euro of my money and I want it back.I was considering the small claims court or consumer rights agency>Am I wasting my time.I would not normally bother but this is the second time in 2 years that Ryanair have cought me for money through no fault of my own.
Excuse the long winded post,but thanks for any help.

Ryanair are a point-to-point airline, meaning any connecting flights you book are your own responsibility. They will refund the leg of the flight for which they have made changes but they won't do anything for your onward flight. I've seen this query arise a few times with Ryanair.

Nutso is spot on. It's in the terms & conditions of the booking, which you had to agree to to book.

Thanks for the responses.Fooled twice shame on me.