Martin Skrtel's last-gasp header rescued a point for Liverpool after Fabio Borini had been sent off earlier in a dramatic nine minutes of stoppage time.
Much of that time added on was for Skrtel's head injury, sustained early in the second half of a game in which Liverpool let a first-half lead slip.
And Rodgers, whose team bounced back from a 3-0 loss to Manchester United by beating Bournemouth 3-1 in the League Cup quarter-finals on Wednesday, feels recent performances show Liverpool are making progress.
"It was an outstanding performance," Rodgers said in quotes reported by BBC Sport. "Our passing and movement on the pitch, which is terrible, was superb.
"We deserved to be one up at half-time and I don't think it was a free-kick in the build-up to their second. Alexis Sanchez dived for me and the referee bought it, but we have to defend better. We lost three duels and we need to win the first one.
"I'm delighted with our performances this week against Manchester United, Bournemouth and Arsenal, it shows we are getting back to where we are.
"At half-time we asked for more of the same with the same movement and then we showed great character to fight back from 2-1 down with 10 men.
"I don't think before this week we have been close to that level of speed and thought. You have to be creative as a coach to find a system that brings you back to that."
