But Arr remained upbeat and says Warriors will now focus their attentions on next Saturday's crucial clash with Sale.
He said: "We're treating every game as a cup final and Sale next week is massive. We showed against Leicester last Friday how good we can be at Sixways.
"Sale are a decent unit but we'll certainly target that game and we will go all guns out to try and win it."
Warriors contested with Northampton for most of the clash, with the visitors producing some fine rugby.
And Arr insists his side will continue to give their all to try and beat the drop from the Aviva Premiership.
He continued: "We put up a good fight and we were in the game for over an hour.
"We showed we're capable of playing some really good rugby, especially with Lemi's try but ultimately ill-discipline cost us.
"Moving forward now, in every single game we play we want 100 per cent emotion and work-ethic."
The scrum-half also says he is delighted to have signed a new contract with Warriors, having been at the club since his schooldays.
And the number nine admits his decision to remain at Warriors is because of the good times ahead he expects.
He concluded: "I was pleased to put pen to paper and sort my future out. It was really special for me to sign with Warriors having been around this club for so long.
"I genuinely believe that, although we face difficult times at the moment, we will progress in the future and make Worcester a special club.
"The fact that Chris Pennell, Alex Grove and Ravai Fatiaki have all signed new contracts show we have total belief in Dean Ryan and his team and we want to be a part of it."