The Hoops had an offer for the striker accepted by Celtic earlier this week, with Norwich following suit soon after.
Hooper spoke to both clubs but opted to join the Canaries on a four-year contract this afternoon, citing a chance to play in the Premier League as a decisive factor.
Redknapp told Sky Sports News: "You can't hang about. I could write a book about players that I have signed and lost over the years.
"Deals have got to be done quickly and it dragged on probably two-and-a-half months altogether that deal. It was miles too long. It should have been done, but that's how it goes, we learn from that one and move on. We can't make that same mistake again.
"If we're after a player and we really want him and he wants to come. Because the boy wanted to come, I don't care what anybody says, he was coming to us, but I just think that it seemed to be a bit of a mix-up with the deal and everything. Never mind that's how it goes."