The winger said: "In the second-half the boys gave everything and they came back. We fought hard and no one can fault the boys - they played their hearts out.
"The spirit was high on the pitch. Everyone just kept encouraging each other. Everyone really wanted to close this game out. Everyone was confident we could get the win. But it didn't go our way.
"The sprit we have in this team will stand us in good stead next season. We are a close-knit squad and that will only help us."
Warriors found themselves 14-6 behind at half-time before turning the game around thanks to tries from Matt Kvesic and Drauniniu.
Richard Hill's men went ahead in the second-half but couldn't find an answer to Exeter's late winner.
Drauniniu continued: "The last minute is always the hardest. The other team are just coming at you again and again. We're gutted but we're learning things and we know what we must do.
"We need to close the game off early. But the only thing we can do now is keep our heads up and keep pushing on."
With three games remaining this season, Drauniniu has targeted scalps in the form of Premiership giants Saracens and Harlequins.
He added: "We're just looking forward to every game as it comes. We'll be coming in and playing our hearts out till the end.
"We want to do well against the big boys - we've already beaten Saracens once this season.
"Our signings for next season will encourage the kind of rugby we want to play. We'll have a good squad and it's all about how we progress as a club."