Initially he made a good start to life at the Emirates Stadium, playing 23 times in his first Premier League campaign at the club - one more appearance than he managed at Southampton the previous year.
Carragher also added that he feels that the Manchester clubs and Chelsea are the only teams that can win the League this season.
"We won our first game of the season at home and I thought we'd be alright and then went to Crystal Palace".
"Harry came in at half-time and took three men off, put three at the back, five in midfield with three rolling attackers and we won 3-2".
Redknapp's most notable piece of silverware in a long and respected career in English football is the 2008 FA Cup triumph with Portsmouth.
Former Arsenal midfielder Paul Merson claims that if Arsene Wenger had the tactical nous of former Tottenham Hotspur manager Harry Redknapp, he would lead the Gunners to the title.
Arsenal are fifth in the Premier League with 13 points from seven matches.
The pair have endured a frosty relationship over the years with Merson constantly bemoaning Arsenal and Arsene Wenger on Sky Sports.
When asked to give his thoughts about the 49-year-old pundit coming out of retirement to play for Welsh fourth-tier team Caerau, Wenger responded: "We speak about professional football here".