The Hornets were 1-0 up at Vicarage Road with Ismaila Sarr on target, only to concede three times in quick-succession.
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Relegation-threatened Cardiff netted their goals through Kion Etete, Cedric Kipre and Sory Kaba, with the victory lifting them out of the drop zone.
Wilder was left raging post-match following his side's debacle, starting off praising players, before then producing a six-minute rant.
"When we went 1-0 up, you might have seen I got a message on to Hamza (Choudhury) and said: 'Nobody changes the script, just do what we're doing, keep doing it, keep moving the ball, keep opening them up and finding the spaces,"' he said.
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"It could have been a good night for us. The atmosphere before was great. I think people enjoyed the start we made. And then all of a sudden, it just went off plan."
The 55-year-old then criticised his team for the way they let the Welsh side back into the contest.
"We allowed the opposition to get back into the game, they sniffed we were weak mentally and physically, and scored three," he added.
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"All of a sudden everybody wants to flick it and do their own thing. People are playing out of position, hitting cross-field balls… you lose your rhythm quickly.
"Basically, you say to the opposition: 'There you go, there's an opportunity to get back into the game'. And they took it. We gave a daft free kick away and we can't defend set pieces.
"Players haven't got the courage to dig each other out, they've not got the courage to say: 'Get off my toes and go and play in your position', and that's basically because they're individuals.
"It's quite difficult to analyse 20-odd players. Some might just be not bothered and underneath their breath saying: 'I'm not bothered, there's no consequence for me as a player'.
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"Some might care, they might take it on board. Some might not even know who I am. But I know who I am. I know what principles I've got and I know what I've achieved through being a team player and a team man.
"I'll keep being that team man. I'll sacrifice everything to be involved in the team.
"I don't think anybody will be able to get a tune out of this firm if they go individual."
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Wilder was then asked if he believed Watford, who are know for regularly chopping and changing bosses, were unmanageable.
"I think it's a struggle. I think six have had a go now recently. It's a struggle and it's been difficult for the supporters.
"Two relegations, a mid-table finish and the Covid season, where it was good. I don't think it is unmanageable, but there are certain things that really have to change, in my opinion.
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"There has been the model and there has been success with it. The owners might try and recreate that.
"I personally think the supporters want something a little bit deeper than maybe what's happened.
"I'm not going to talk about myself. It's not about me or what I'm going to do next year.
"I'm not going to get caught up in any of that regarding me, I don't think it's right at this particular moment to talk about my future."
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Wilder is likely to leave his post with the Hornets at the end of the season.