The result means Arsenal are in 15th place, their worst start to a season since 1974-75.
"It's not good enough," Tierney said. "There is no way to disguise it. It's terrible, to be honest. It's not what we are, not where we are as a club.
"It's not what the fans deserve, it's not what the manager deserves, it's not what the board deserve. It's us players that need to take responsibility for this.
"We have got a great manager and we believe in him 100%. The blame is on us, nobody else."
Arsenal have only managed two wins in 10 Premier League games and have gone 12 hours and 32 minutes without scoring from open play.
"Everything is going wrong. We are working on the right things, we are doing the right things in training, we are working as hard as we can, but just things that can go wrong are going wrong," Tierney added.
"That happens in football. It is the lowest we have probably all felt in our careers and nobody is going to help us except ourselves.
"Confidence is massive in football with everyone. When everyone is out to get you of course confidence is going to be low, but we can't let that affect us. We can't use that as an excuse.
"We are Arsenal. We need to be better than this and we are not performing up to standard. We need to be better throughout the full game. We need to take chances, we need to score goals.
"It's Arsenal. It's just not good enough."