Renard left the Chipolopolo post on Monday to take charge of struggling French Ligue One side Sochaux.
Chilumba said in an interview in Kitwe that Renard’s replacement, Patrice Beaumelle, should be given all the support he needs.
“I think he did his part and I think we just have to move forward and we should not say bad things about him. Of course he won the Africa Cup and to me that is a big credit,” Chilumba said.
Renard, who won the 2012 Africa Cup and 2013 Cosafa Cup, signed a season-long deal with Sochaux after two years in his second tenure as Zambia coach.
“We just have to move forward; whoever is going to get the job we just have to support him whether he is a local or expatriate,” he said.
Renard’s long-serving assistant Beaumelle has been handed the reins in an interim capacity.
“I am comfortable with him (Beaumelle), he is also a good coach,” Chilumba said.
“It is okay if they are talking about continuity but they must also consider a local as an understudy.”