Redknapp said that he thought the response from his side after the goal meant that they deserved something from the game.
"I felt to go a goal down within a minute, we showed fantastic spirit," Redknapp said to ESPN. "We hung in there and we could have gone under after conceding a goal in a minute.
"After that I felt we were every bit as good as them and could easily have got a result. I thought it was an excellent performance and the spirit was first class.
"What more could we have done? We conceded an early goal against a team that has gone to Bayern Munich and won this year."
The win keeps Arsenal in second place in the Premier League.