The Potters dismissed Pelach following a run of nine matches without a win in the Championship.
Pelach only had 19 games in charge of the club having been appointed in September following the sacking of Steven Schumacher.
In that time, Stoke won just three matches seeing them fall from 13th to just above the drop zone.
Their latest result was a 2-0 defeat at home to Leeds United on Boxing Day, a loss that has left them in 19th place in the table at the midway point of the season.
Speaking to Stoke's official website, sporting director Jon Walters said: "Narcis is a talented coach with huge potential, he works relentlessly hard and I have no doubt that he will go on to achieve success in the future.
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"However, with the way results and performances have been in recent weeks, we have to accept with hindsight that he has proved not to be the right fit for this club at this time.
"I take full responsibility for that and I'm absolutely determined that we will now make the right choice to take us forward.
"Every decision we make is driven by our love of Stoke City and absolute determination to bring success to the club."
Pelach then released a statement on Saturday, posting on X: "It did not go the way I wanted and I am sorry for that.
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"I did everything I could and unfortunately my best was not enough.
"I am really grateful to John Coates and John Walters for giving me this opportunity.
"I am sending a big thank you to the players who have given me lot of respect, affection and enthusiasm. Also, to the staff for the support received.
"I genuinely wish Stoke City and the fans all the very best. Thank you."
The club will now be looking for a new permanent manager but for now, they've named a caretaker boss.
For their clash against Sunderland on Sunday afternoon, ex-Potters centre-back Ryan Shawcross will be in charge.
Shawcross, who made over 450 appearances for Stoke, is the club's current under-21's head coach.
The former Premier League defender will step up to manage the first team, alongside Dean Whitehead, Alex Morris and Darren Bechet.
When confirming Shawcross' role, the club also revealed that Goalkeeper Coach Paul Clements and Performance Analyst Harrison Glew had left the club with Pelach too.
Pelach was Stoke's sixth managerial appointment in just over six years, with the club turning over managers quickly.
It is also the Potters' third sacked in a year after dismissing Alex Neil in December 2023, Schumacher in September and Pelach now.
The 2-0 Boxing Day loss to Leeds followed another 2-0 defeat to 10-man Sheffield Wednesday last weekend.
Before that, a 2-2 draw with fellow Championship strugglers Cardiff followed consecutive 2-1 losses to Luton and Sunderland.
Stoke last won a game on November 6 as they picked up three points away at Blackburn.
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They are next in action when they host Sunderland with Shawcross on the touchline.
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Before they then travel to face Burnley at Turf Moor on New Year's Day, with Shawcross potentially still in charge.
A trip to face bottom-of-the-table Plymouth follows three days later.