Newcastle recorded their third consecutive defeat after crashing out of the Carabao Cup in the second round on Wednesday night.
A resilient Burnley kept the home side at bay for 90 minutes before winning 4-2 on penalties.
The result continues a disappointing start to the season for Steve Bruce's Newcastle, having lost their first two Premier League ties against West Ham and Aston Villa.
Bruce said he thought his side "deserved to win the game".
Third-choice goalkeeper Freddie Woodman, who saved a Josh Brownhill penalty, is hoping his team's luck will soon change.
The 24-year-old was thrust into the limelight earlier this month following Martin Dubravka's foot injury and Karl Darlow's COVID-19 diagnosis, which caused him to be hospitalised.
Despite saving a Michail Antonio spot-kick against West Ham, Woodman is yet to finish on the winning side since entering the starting 11.
"It's the life of a goalie, isn't it? " Woodman told NUTV after Wednesday's match.
"People keep telling me things are going to change soon and luck will be on my side. Hopefully, that's sooner rather than later."
Woodman had little to do during normal time, while his opposite number Wayne Hennessey made a succession of dramatic saves.
The Burnley keeper kept the match goalless with crucial stops from Jeff Hendrick and Dwight Gayle. He then saved penalties from Allan Saint-Maximin and Miguel Almiron in the shootout.
"Their goalkeeper, Hennessey, I thought he was brilliant. He made some really top saves," Woodman continued.
"But saying that, I think we can take a lot of positives from the game especially the way we played in 90 minutes, so we're disappointed, but there's lot to take from this game.
"We have to pick ourselves up and go again on Saturday and take the positives from this game into the Southampton match."
Newcastle play Southampton at 3pm on Saturday at St James' Park.