Allardyce's side are now six games without a win - but Steven Taylor's goal on the hour earned Newcastle a deserved point at St James' Park, cancelling out Emmanuel Adebayor's early goal for the Gunners.
Allardyce was pleased to see his players rewarded for their efforts after what he felt was an unlucky 3-1 defeat against Blackburn last time out.
"I think we've lost the last two home games poorly and it was difficult to take for us all.
"I didn't want to see confidence ebb away. I then saw a performance at Blackburn but not a result, tonight I've seen a performance and a result."
The former Bolton chief even believes his team were close to claiming the win thanks to some attacking play in the closing stages.
"Once we scored we saw Arsenal on the back foot and they could not get going.
"We pursued an equaliser and then pursued a winner for the entire 45 minutes. I feel very unlucky not to have won the game because we had the chances and could not find the finish."