Captain Findlay Williams praised Swansea’s resilience after fighting back from 20-8 down to beat Exeter.
The match was dominated by Exeter in the first half before Swansea took control of it after the break.
“We played poorly in the first half but played very well in the second,” said Williams.
“The key to our comeback was definitely our mental strength and special praise goes to Steve Howorth, Tayo Adesanya and Rob Horshall for their great performances.
“Last season we were unbeaten and even though we’ve lost one already we still want to win the league.”
In the opening minutes Exeter made the breakthrough, with Swansea being penalised within ten yards of their try line by the referee.
After a quick bit of thinking by the wide man the ball was planted over the line.
Following a try by the Swansea side, Exeter continued in a similar fashion, scoring two more tries and converting a penalty kick.
The kicking performances from both sides lacked any consistency with only six of the ten kicks converted.
Swansea also lacked any sense of fluidity in their passing with the ball frequently missing the intended target.
The match was somewhat dampened just before half-time when an ambulance was needed for an Exeter player who had a suspected broken arm, but it was later confirmed to be a dislocated elbow.
The second half began much more positively for Swansea as they displayed a much tougher defensive proposition for Exeter.
The home side did not allow their opponents to score again, in a half totally controlled by Swansea.
They made the most of their possession, turning the ball and making the most of their chances, breaking well.
In the space of twelve minutes Swansea successfully scored three tries to turn the game on its head.
Swansea also converted two of the three kicks as well as a final penalty kick scored in the 66th minute.
The performance of Adesanya was particularly impressive; he scored two tries and converted two kicks for Swansea.