The Northern Irishman - who left the club on Tuesday by mutual consent - believes his former assistant Jimmy Nicholl and veteran full-back Garry Hay should be given the job of leading the Rugby Park side.
Killie have yet to comment on the future of former Raith manager Nicholl but Shiels told Press Association Sport: "I would recommend Jimmy to manage the club and Garry Hay to be his assistant."
Shiels was axed as manager after Killie finished ninth in the Clydesdale Bank Premier League.
A four-match ban handed to the 57-year-old following outspoken media comments - two of which were suspended - was also taken into consideration by the club. But Shiels insists he only ever tried to protect the Ayrshire outfit when he expressed his bullish views to the press.
He said: "I'm heartbroken but that is football. It's hard to take but I will just have to get on with it and try and get another job somewhere.
"I think I've left Kilmarnock in really good shape. We have got stability and I've built the foundations. But I feel that I've been the victim of falling in love with the football club. I tried to over-protect the club and that was my biggest weakness. I just want to apologise to the supporters for that."
Shiels stepped up from assistant manager to replace former boss Mixu Paatelainen in April 2011. He led the club to back-to-back victories over Rangers in 2012 and secured the club's first victory at Celtic Park in 57 years in October of that year. But his biggest achievement as Rugby Park boss came seven months earlier when Killie stunned the Hoops with a 1-0 win to claim the Scottish League Cup.
However, a clause in a contract agreed with chairman Michael Johnstone allowed the club to dismiss him if they failed to finish out of the top flight's bottom four. And they used both that and his latest disciplinary problems as the basis for the decision to go their separate ways.
A Killie statement said: "The club wishes Kenny every success in the future and thanks him for delivering the League Cup to Rugby Park in 2012."