Rodgers, who originally left South Wales for the Liverpool job in 2012, held talks with City supremo Jenkins at the time but was not handed the position.
Speaking to BBC Sport, the 54-year-old opened up on his hurt of missing out on Rodgers, while also insisting that Carlos Carvalhal - the latest manager to arrive at the Liberty Stadium - can get the best out of the current crop.
"I wanted him back, I spoke to him three times," he said. "That would have been the biggest thing that we, or I, should have done differently. I don't think any of us were happy with it and how it panned out or the way it ended. With more time, probably we would have made different decisions.
"We've got to buy and sell players to try to fund any new acquisitions, but at that time at 2016 was very simple, we had no one shareholder that could cover our financial position if we got relegated."
"I don't think we have seen the current squad we have play to its full potential. It will be interesting to see if Carlos can get more out of them and then we can have a more balanced view of how our summer worked out.
"There will be money left over from the summer. That money has not gone anywhere. If we wanted to go beyond that, it's what we have always done and how we have always worked."