Arsene Wenger has refused to press the panic button despite the growing gap between Arsenal and the Premier League pace-setters.
Arsenal qualified for the knockout stages of the Champions League in mid-week, but are losing ground in the battle to ensure an automatic place in next season's competition.
They are 10 points behind leaders Manchester United and six behind West Brom who were in the third automatic spot after Saturday's matches.
Fans also chanted 'you don't know what you are doing' after a late substitution saw Olivier Giroud replaced by Francis Coquelin.
But Wenger appears unconcerned and pointed to the early part of last season when Arsenal were written off but still clinched a Champions League spot.
He said: "I would like to show what you (the media) wrote about us last year in September, October (when Arsenal were struggling).
"Why should we panic? We will worry about our next game and we will play that.
"We are focused on the next game. Don't worry for and about us too much."
Wenger believes playing a third game in quick succession, after the wins over Tottenham and Montpellier, was the reason for his side's lack of spark.
He also opted to rest Jack Wilshere after a recent run of matches following his lengthy lay-off.
He said: "I think it (the performance) was a result of fatigue and we had not 100% recovered from playing on Wednesday night (against Montpellier).
"After a Champions League game, and then you have to play away from home, it can happen that you draw.
"We could have won the game, we could have lost the game. You have to respect Aston Villa as well.
"We certainly had the right attitude but there was a lack of sharpness and fluency in the final third of the pitch."
On midfielder Wilshere's omission, Wenger said: "It was the sensible thing to do. He has played a lot of games recently and is coming back from a long spell of not playing.
"It's not the thing you want to do, play him or bring him on when he's tired. It made sense for him not to play."
Villa keeper Brad Guzan had only one save to make during the 90 minutes as his side secured the point which moved them out of the bottom three.
Villa manager Paul Lambert watched the game from the stands while serving a one-game ban, but could see encouraging signs amongst his crop of young players despite their current league position.
Striker Christian Benteke further enhanced his growing reputation, while defender Ciaran Clark is adding to his stature with every game.
Lambert said: "We've just played the two Manchester clubs and Arsenal in succession, a tough ask for anyone, and the performances have been excellent.
"Even at City (when Villa lost 5-0) we were in the game until a controversial penalty and the point against Arsenal was well deserved.
"This is a young team and they will make mistakes and I've said from the start that is a long project and things will not happen overnight.
"But we've come through these three games, have got goals in the team and, with the way we are playing at the moment, we will be fine."
Villa now face a crucial home game with fellow strugglers Reading on Tuesday and will hope skipper Ron Vlaar recovers from the injury which led to him being substituted against the Gunners.
Lambert said: "It's his calf. We will train and see how he's feeling."
Villa are also trying to solve the groin problem which has dogged another defender in Richard Dunne all season.
Lambert said: "He's seeing the doctor. We will try to get to the bottom of the injury, which is a bit mysterious. We are trying everything we can to sort it."