Hello Nick,
This is a common problem that happens with pilots who do not activate their flight plans properly.
Did you get a squawk code from the Web UI?
To access the replay, you would have to go to your flight plan briefing page. When it is correlated properly, you will see the replay button on the top right corner. But if it wasn't correlated (i.e. you got a squawk code and departed within the 2-hour window) you will not see that button.
In addition to that, your recent flights show the "connections" and not the flight plans. So if you got disconnected, it might show a separate "connection" that starts from mid-air onward, hence the "ZZZZ" you see in your origin.