De Villiers, the top 50-overs batsmen in the world, is back home to be with his wife for the birth of their child.
He was suspended for one game earlier this week following an incident in Australia, after which Cricket South Africa decided to let him stay at home for the rest of the series.
"When a team loses a pillar of strength like AB, it becomes the responsibility in the first place of the other experienced players to take the lead," McKenzie told the Afrikaans daily Beeld here today.
Asked if South Africa had become too dependent on De Villiers in the past year, McKenzie said: "I don't think the team is concerned about the depth available to it. The actual issue is Faf du Plessis and JP Duminy must lift the run taking burden from Hashim Amla's shoulders."
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The veteran said nobody had questioned the quality of the other players, but expressed a concern that the selectors might not be looking at addressing the imbalance in the side that caused their fallout in the World Cup in Australia earlier this year.
"In the longer term, there is room for just one all-rounder. I would choose my preferred candidate and let him play through the entire series."
CSA had earlier said that it would allow newcomers some opportunities during the Bangladesh tour.