The Ivorian left for Lille after winning the Champions League, and has suggested whatever Roberto Di Matteo does, the Russian billionaire will always be No.1 at Stamford Bridge
The Ivorian left Stamford Bridge for French side Lille in the summer after winning the Champions League in his last appearance for the club, and states that the Russian billionaire had a positive influence on the team.
And Kalou suggests despite hiring and firing managers at will in a search for success, Abramovich left the players with no doubts as to who was truly in charge at Stamford Bridge.
"As a Chelsea player, you have to take responsibility, and it's the role of the owner to remind everyone the only boss is him," he told Mirror Sport.
"The owner used to remind us very well and it worked every time. He came twice to tell us. Once in Carlo Ancelotti’s time and we won the Double, and he came again after Andre Villas-Boas was sacked, and we won the Champions League.
"The Chelsea players are not scared of the owner. But he doesn't talk a lot, so when he does you listen."
Kalou feels Abramovich was integral to the success of the club, saying the Russian was involved with the team and the players despite the constant rotation of managers, with some players enjoying a close bond with the owner.
"If you see the results, it is positive that the owner is involved. He has the idea 'I want to run this club, I want things to work'. He wanted to win the Champions League and then he won it, so it was worth it.
"Maybe if the owner backed off it won’t work any more, because when you invest in some ideas you really want them to work. Sometimes you have to remind people 'I'm the one in charge'.
"He was excited around the training ground and some of the players have a special relationship with him. He always made sure whatever we needed we had it, and you cannot ask more from an owner than what he did for us."
The 27-year-old forward said being at Chelsea was the best period of his career, and he regards Jose Mourinho as his best manager - although Roberto Di Matteo runs him close.
"The owner always brought the best manager and players to the club, and he helped everyone to win something. I won whatever a player could expect to win, so that experience was the best of my career and any other player would dream of having that. I'm going to say Jose Mourinho was probably the best one, and also I had a wonderful six months with Robbie [Di Matteo]."