Attenborough, who was a former Chelsea director and life president at Stamford Bridge, passed away at the age of 90 last month.
In the programme for Saturday's match against Swansea City, Terry wrote: "We have lost a huge Chelsea fan, our life president but, more importantly a tremendous man.
"Until the past few years he and his family were always here supporting us and he would come down to the dressing room and the manager always welcomed him. What he did in the film world was unbelievable and films I watched growing up my kids now watch and they are still greats.
"He was a true gentleman and will always be remembered. He meant the world to us and I know Chelsea Football Club meant the world to him."
Chelsea wore black armbands and held a minute's applause for Attenborough before securing a 4-2 victory over Swansea at Stamford Bridge.