A victory would have been enough for either nation to progress to the quarter-finals, but they lacked the quality to reach the last eight and Democratic Republic of Congo and Tunisia progressed following their 1-1 draw.
Cape Verde went into the game in second place, but bow out after drawing all three games, with Democratic Republic of Congo leapfrogging them on goals scored.
Zambia, the 2012 AFCON winners, entered the game knowing they had to win to have any chance of going through.
Evans Kangwa and Mukuka Mulenga had clear opportunities to hand Zambia victory late on, but both men were unable to finish.
Incessant torrential rain led to puddles developing on the pitch and it seemed the game could be postponed, but both sides persevered in vain as their tournament was cut short.
The onus was on Zambia to get on the front foot from the off, but neither side looked threatening in the opening stages.
Cape Verde goalkeeper Vozinha breathed a sigh of relief when he spilled Given Singuluma's long-range drive and Kangwa was wrongly adjudged to be offside following up.
Zambia captain Rainford Kalaba then had half a chance to open the scoring when he was given too much space in the penalty area 23 minutes in, but his tame shot deflected wide .
Cape Verde's Garry Rodrigues showed a sharp turn of pace to get down the inside right 10 minutes before the break, then let himself down with a lack of composure by firing off target with a poor finish.
It was Cape Verde who finished the half strongly, though, with Zambia enduring two alarming moments just before the break.
Toni Varela got his header all wrong when he was left unmarked from a Rodrigues free-kick. Winger Rodrigues then delivered a side-footed set-piece which somehow evaded everybody and went out for a goal-kick.
Conditions deteriorated at the start of the second half, with standing water appearing on the pitch as the rain continued to lash down, preventing the ball from rolling in certain areas of the pitch.
The game was allowed to continue, though, and substitute Djaniny forced a save from Kennedy Mweene with a long-range drive that bounced awkwardly in front of the Zambia goalkeeper.
Kangwa resorted to desperate measures when he took a dive in the penalty area and was shown a yellow card 15 minutes from time.
The same player was unable to make contact with Chisamba Lungu's cross three minutes later as Zambia pressed for a winner, while Mulenga also spurned a golden opportunity when firing wide from close range in stoppage time.
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