Spurs travelled to Turf Moor on Wednesday morning for the fourth round clash with neither England international due to be part of the group.
Both players are fit and featured in the 1-0 defeat at Vitesse Arnhem in the Europa Conference League last week, when Nuno left his first XI at home to prepare for Sunday's League game against West Ham, which Spurs lost by the same scoreline.
After the defeat in Arnhem, Winks expressed his frustration in an honest interview and he was subsequently left out of the squad at the London Stadium, where Dele was an unused substitute.
Winks has started just one League game this season and was replaced after an hour of the 3-0 defeat to Crystal Palace, while Dele began the campaign with a series of encouraging performances in a deeper midfield role but his form has flatlined.
He was substituted at half-time of the north London derby defeat to Arsenal, with Spurs trailing 3-0, and has not played a minute in the Premier League since.
Nuno last week admitted that Dele is "not in his best moment" but his latest omission casts further doubts on the future of the 25-year-old at the club.
Both Winks and Dele are desperate for regular first-team football and are likely to consider their options in January if they continue to be overlooked by Nuno.
Speaking in Arnhem, Winks admitted he has no idea how he has gone from England regular to underwhelming for Tottenham's second string and suggested Nuno's decision to leave his first XI at home for the defeat to Vitesse had impacted morale.
Asked if he could make sense of his dramatic fall, Winks said: "No. No, I can’t. But listen, the circumstances are that I’m in this situation.
"Of course [my confidence is low]. When players are not playing well and you only have yourself to blame, it’s difficult. I want to be at my best, firing and playing really well. It comes with games. But ultimately it comes with me performing on the pitch when I get the opportunity.
"If I’m not doing that, then I only have myself to blame. I’m man enough to admit that I need to improve in certain areas. On the contrary, I need to play games and the only way to [improve] is getting minutes and getting that sharpness back."
On Nuno's rotation, he added: "We’re meant to be a team. It’s meant to be competition. It’s meant to be competitive. Everybody should be fighting for [a place in the] weekend games and it’s difficult."
Nuno is under pressure to get a result against the Clarets after his rotation policy backfired against Vitesse and West Ham, and he has described the game as "a final" for Spurs.
"It's going to be a tough match like we expect because Burnley is a good team but it's a good chance for us to improve, knowing that the Carabao Cup is an important competition for us," he said. "We have to go game-by-game and then this game is a final."
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