The Gunners lost to Burnley at the Emirates, their fourth consecutive home loss in the Premier League.
Pressure builds on Arteta as Arsenal remain in the bottom half, just five points above the relegation zone.
Tierney admits there are small signs of improvement, but not enough to jumpstart their season and it’s up to them to repay their manager’s faith.
He said on Sky Sports: “We don’t show the manager what we can do and how much we believe in him.
“In every game there are signs that we are doing a little better but it’s still not good enough. At halftime we have to be in the lead, but we don’t.
Arsenal’s task against Burnley was made more difficult after Granit Xhaka was sent off in the second half.
The Swiss midfielder was fired for violent conduct with the Gunners in the ascendancy.
But Tierney isn’t convinced that going down to ten was crucial to their loss.
“It’s hard to say that the red card cost us the game,” he added. “It was always going to be a lot harder. ”
The Scottish defender, however, insisted on calling Arteta a “great manager” and challenged the players to find the winning formula.
He continued, “Hard work is the only thing [that can fix this], nothing else for that. There are no excuses. There is nothing I can say that will make people believe that anything good will come of it.
“We are lucky to have an excellent manager. We just need to show better on the pitch. ”