Slack Spurs defending allowed Mario Vrancic to open the scoring and only a VAR review to harshly rule out Teemu Pukki's goal prevented Mourinho's men trailing 2-0 at half-time.
Even once the visitors had regained a foothold in the game via Christian Eriksen's free-kick, they shot themselves in the foot at the back once more as Serge Aurier's calamitous own goal restored Norwich's lead.
Harry Kane's penalty eight minutes from time ensured Spurs did not slump to a third defeat in seven games, but they failed to take the chance to leapfrog Chelsea into the top four.
The area of the field with work to do for Mourinho remains obvious and his side have kept just one clean sheet in 10 games since he took over.
Tottenham's season is being chronicled as an Amazon documentary and Mourinho believes the focus of that show should be on his side's defending.
"I think if Amazon wants to do episodes, they will have for sure one episode about our defensive mistakes and the goals that we concede," he told Sky Sports.
"We conceded two very bad goals, the first and the one that was offside but two very bad goals.
"Second half I think we were very, very good with the ball; we create, dominate with play but again the goal (conceded) is a very bad one.
"To score two goals away from home, you have to win. You cannot concede as many goals as we do, but our defensive mistakes are match after match."
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Tottenham could have been out of sight inside the first 15 minutes as Dele Alli fired wastefully over before Kane was denied by a fine save from Tim Krul when one-on-one.
At the other end, Vrancic could not believe his luck as Toby Alderweireld stood off and allowed him to close in on goal before firing low past Paulo Gazzaniga to open the scoring 18 minutes in.
Only VAR prevented Tottenham falling further behind before the break as Jan Vertonghen allowed Pukki to control Vrancic's ball over the top and the Finn finished clinically.
However, Pukki's joy was short-lived as he was harshly adjudged to be offside after a VAR review.
"The disallowed goal was tough to take," said Norwich manager Daniel Farke. "It's not in the sense of the game."
Mourinho showed his displeasure with Spurs' first 45 minutes by making two half-time substitutions and changing his system as Lucas Moura and Davinson Sanchez replaced Juan Foyth and Vertonghen.
The Portuguese got the upturn in performance he desired as the visitors were level 10 minutes into the second half after Jamal Lewis handled on the edge of his own area to prevent Kane a clear sight of goal.
Eriksen has been a peripheral figure both under Mourinho and Mauricio Pochettino earlier in the season due to his contractual standoff with the club that will most likely see the Dane leave on a free transfer in the summer.
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But he produced a timely reminder of his quality by curling the resulting free-kick into the top corner.
Moments later, the ball was in the Norwich net again but this time the offside flag went in the hosts' favour as Alli's classy finish was ruled out.
Just as Tottenham seemed to have taken control, the tide turned again in the other direction as Norwich retook the lead in comical fashion.
Aurier turned the ball into his own net after the ball ricocheted into his path from Alderweireld's tackle on Pukki.
Spurs laid seige towards the Norwich goal in the final quarter and not for the first time this season Farke's men were unable to see the game out.
Kane was wiped out by Zimmermann as he cut inside and the England captain picked himself up to dispatch the resulting penalty.
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