It is of no interest to them. You had two separate contracts of carriage with no correlation between them (other than to yourself). If you can find compensation within the terms and conditions of the first contract, that is where your remedy would lie. For example if the flight was late for defined qualifying conditions you might be eligible for "EU261" redress.
Had you booked with a non point-to-point carrier as one through ticket (BA/IB etc.) you would likely have been rebooked on the next available service at no extra charge.
You chose to risk the first flight arriving on time to satisfy your requirement for being able to depart on the second and wholly (for contractual purposes) separate flight. The "expectation" (although they will have none) is that you left sufficient time between the arrival of the contracted service and whatever onward arrangements you had made, in order to mitigate your own level of perceived risk.
The "simple" answer (fraught with a myriad of potential caveats,) is to allow at least 4 hours between the flights. That way, there is a reasonable chance that EU261 compensation for a delayed flight, will mitigate your losses for having to book another (likely expensive) flight, or overnight accommodation. Similarly, book an origin to destination ticket on one carrier (for contractual purposes) right through to your intended destination.
If you "know the rules" then you must know the risks.