Chelsea legend Terry completed a free transfer to Aston Villa on Monday despite interest from the likes of Bournemouth, Swansea and several MLS and CSL sides.
Birmingham alos made the 36-year-old an offer and Reknapp admits that he may not have done all he could to convince Terry that his future lay at St Andrews.
In an interview with 'talkSPORT', Redknapp explained that "I probably take the blame myself, I didn't really chase after John"
"We made him a great offer but in the back of my mind I always had this thought about the budget and the players' wages."
"I thought: Do I put all my eggs in one basket or do I bring in four or five players that might help improve the team?"
"So we made the offer and then I stood back and maybe Steve (Bruce) was a bit more active in trying to get John than I was."
"But he is a top player and he is a big signing for Villa for sure."