Mike Garrity fielded a youthful side in Chester due to the absence of several of his regular starters, with the likes of captain Harry Wilson, Ben Woodburn and Trent Alexander-Arnold unavailable ahead of the first team’s game against Bournemouth on Wednesday.
And Norwich proved too strong, with Ebou Adams’ early long-range strike enough to seal their place in the last four.
The young Reds will now turn their focus to the final four games of their Premier League 2 campaign, with a trip to Southampton in a week’s time their next assignment.
Norwich started adventurously and both Conor McGrandles and Bernard Ashley-Seal missed presentable opportunities before Adams put them in front with a fine effort in the 10th minute.