The scores were already level when Emmanuel Adebayor was sent off for a second yellow card after half-time.
Lee joked to the club's official web site: "His phone bill will be quite big! Technology meant it was never going to be a problem. It's testament to his professionalism because he was in a lot of pain.
"Our hope now is that he can settle down for a while and get himself 100 per cent right so that he's ready for the really busy schedule that's coming up."
Asked how Benitez had responded to the result, Lee added: "He was pleased. He wanted the lads to know what a good point it was against a very good football team."
He explained: "There's all kinds of cliches but we'd have settled for a point before the game. The lads are a bit disappointed but great credit should be given to Arsenal for the way they fought when they went a man down.
"Once they went a man down they organised themselves right and made sure they kept shape and kept tight. We worked hard to use a numerical advantage but we don't feel we did that - that's maybe why there's a bit of disappointment among the lads.