He said: "When you're chasing a game it's always a case of getting the points before time runs out.
"When I got the two tries I believed we could come back but obviously that didn't happen because they kept the ball well.
"A lot of the damage was done in the first-half. I'm sure it was an entertaining game for the fans but it was disappointing from our perspective because they came away with the points."
Despite the victory, London Welsh will be playing in the RFU Championship next season after finishing bottom of the table.
And, according to Drauniniu, it will be disappointing to see his former club plying their trade outside of the top-flight next season.
He continued: "London Welsh are a good side and it's not nice to see them get relegated. They didn't get a break and it's a shame that they're in that position but that's rugby and someone has to go down. I wish them the best of luck next season."
Drauniniu and his teammates will now have time off before returning to pre-season training in June.
And this season's joint top try scorer insists the break will refresh the side before the hard work begins again.
He added: "The next month gives the players an opportunity to go away, get away from rugby and come back for pre-season refreshed.
"Everyone will be looking to hitting the ground running when Dean comes in. He's got a good reputation and he'll be trying to get us up the league."