What had been a perfect week ended on a disappointing note as a late fightback wasn’t enough to take the Clarets into the fifth round of the FA Cup for only the second time in nine years.
Back-to-back wins have breathed fresh life into the Clarets’ Premier League campaign but there will be no extended cup run to go with it after top-flight rivals Norwich set aside their recent struggles to go into Monday’s last-16 draw.
Goals from former Blackburn Rovers defender Grant Hanley and Josip Drmic inside the space of five minutes early in the second half were enough to take the Canaries beyond round four for the first time since 2012.
The Premier League’s bottom side deserved their success as the Clarets were unable to lift themselves sufficiently off the back of their mid-week heroics at Manchester United.
But Burnley at least didn’t go out without a fight as a superb strike from Eric Pieters threatened a comeback and a replay neither club arguably needed during their ‘mid-winter’ break early next month.
Both sides mixed it up following their Wednesday night efforts in the Premier League, but they were still senior line-ups on show.
And there was no shortage of quality displayed in an entertaining first half that somehow ended goalless.
Norwich set the tone inside the opening 10 seconds when straight from the kick-off Tom Trybull slipped in Drmic for a chance the Swiss rolled the wrong side of the post.
The Canaries played with a freedom the break from their relegation fight allowed and thought they had gone ahead after a quarter of an hour.
Another slick move allowed full-back Sam Byram to burst into the box and after his shot beat Joe Hart, only James Tarkowski will know he managed to get back to somehow block on the line with his chest and deflect the ball past the post.
Hart did make decent saves to keep out long-range efforts from Onel Hernandez and Lukas Repp, while Tarkowski continued to wage what looked like a one-man battle at times with a superb tackle to deny Mario Vrancic.
Drmic then missed again when he dragged his shot across the face of goal to book-end a half which had also brought its fair share of chances for the Clarets.
The best of them came just six minutes in when Jay Rodriguez passed up the opportunity to enhance his cup pedigree.
Rodriguez had scored nine times in his last 13 FA Cup ties, including three in three across both spells as a Claret.
But after Chris Wood had delivered the ball perfectly into his path, the striker was unable to repeat the goal he scored when these two sides met for the only previous time in the competition, shooting too close to Ralf Fahrmann, who saved well.
Robbie Brady, one of five starters returning to the Burnley ranks, looked determined to score against his former club with three efforts that all went close, notably one he skidded just wide of the far post after taking an Erik Pieters pass perfectly in his stride.
And Tarkowski couldn’t be kept out of the action as he headed an Ashley Westwood header against the bar.
The Clarets then started the second half on the front foot but found themselves behind eight minutes after the re-start when old foe Hanley headed home a Vrancic free-kick to claim his first goal in almost 18 months.
And Vrancic was then involved again as Norwich quickly doubled their lead to put a foot in round five.
His cross was flicked goalwards by Rupp and although Hart palmed his effort away, the ball dropped for Drmic to tap in from close range.
Marco Stiepermann then missed a great chance to wrap it up for the visitors and with 25 minutes to go Dyche made a double change, Jeff Hendrick sending a low shot skimming just wide with one of his first touches after coming off the bench.
It looked increasingly as though it wouldn’t be Burnley’s afternoon but another cup cracker from Pieters suddenly delivered fresh hope.
The full-back had scored his first goal for the club with a spectacular effort in the Clarets’ third-round win over Peterborough and he repeated the trick with a sweetly struck left-footed volley which flew into the bottom corner from 16 yards out.
That left the Clarets the best part of 20 minutes to try and find a leveler.
But despite the introduction of Dwight McNeil they were never able to build up a sustained head of steam.
And it was the Canaries – gaining some compensation for their league defeat at Turf Moor in September - who went closest to scoring again when the trickery of substitute Teemu Pukki almost brought a third goal in stoppage time.
Burnley: Hart; Lowton, Tarkowski, Long, Pieters; Lennon, Westwood, Cork (Hendrick 65), Brady (McNeil 79); Wood (Vydra 65), Rodriguez. Substitutes: Peacock-Farrell, Taylor, Dunne, Goodridge.
Norwich City: Fahrmann; Byram, Hanley, Zimnmermann, Lewis; Trybull, Vrancic; Rupp, Stiepermann (Duda 81), Hernandez (McLean 84); Drmic (Pukki 88). Substitutes: McGovern, Aarons, Tettey, Martin.
Booked: Zimnmermann, Hanley
Referee: Michael Oliver