No this is normal. In real life this is the same...
The top three places in the Premiership go to Champ League. The FA cup winner gets the last Champ League spot, no matter where they finished. The League Cup winners get a Euro Cup spot.
This is when it gets confusing...
If the League Cup winner has already qualified through the
Prem to the Champ League, the Euro Cup spot goes to 5th or 6th. If the FA Cup winner goes through to the Champ League already through the
Prem, the Champ League Spot goes to fourth. The FA Cup runner up gets a EURO Cup spot no matter where they finish. If the runner up is in the top three or four that spot is passed on to 6th or 7th place.
I warned you, but this is how it works IRL. The Champ League winner has nothing to do with it.