The Scarlets can still quality for the Pro14 play-offs next week after beating the Dragons, but they need Connacht to do them a favour.
The Ospreys were on the verge of victory despite George North's early red card, but Ashton Hewitt's try salvaged a draw for the Dragons.
The Dragons have added Jamie Roberts to their squad ahead of their return to Pro14 action this month.
A five-week break has been implemented in the Premiership, with the Champions Cup and Challenge Cup quarter-finals pushed back.
Matthew J Watkins won 18 caps for Wales in the 2000s, before battling cancer, and his death left his former clubs "deeply saddened".
Benetton Treviso were prevented from playing at home last weekend because of the coronavirus, but returned to action by beating the Dragons.
After losing to Ospreys, Ulster bounced back by defeating Cheetahs, while Glasgow Warriors beat Dragons to move into third in Conference A.
The Ospreys claimed only their second Pro14 win over the season at the expense of high-flying Ulster in a stormy Swansea.
Ospreys were boosted by George North's return but still could not see off Dragons in Pro14.
A move to the Ospreys or the Dragons is reportedly on the cards for Rhys Webb after Toulon agreed to release him from his contract early.