The Magpies fell behind after Ricardo Pereira's opener before United were reduced to ten men as midfielder Isaac Hayden received a straight red card before the half time whistle for a foul on Dennis Praet.
Newcastle fell further behind in the second half as Jamie Vardy's brace, along with Paul Dummett's own goal and Wilfred Ndidi's late finish resulted in a difficult afternoon for Steve Bruce's side.
Yedlin told nufc.co.uk: "We're very disappointed with the result. Every single one of us felt like we should have done better. We're going to have to bounce back from that and the Brighton game also and put in a good shift against Manchester United.
"I thought, before the red card, we were pushing on and still looked a threat even when they went ahead. Obviously, when you're playing against ten men and playing against Leicester, who are in great form and push high and press well, it's then quite tough to play against."
The American right-back, who returned to playing action against the Foxes after a lengthy spell on the sidelines through a groin injury, was left with mixed emotions after playing his first competitive fixture since May albeit in difficult conditions.
The defender also heavily praised the 2,650 United supporters who made the long trip to the East Midlands and urged fans to continue their strong backing for Newcastle's next Premier League fixture - a home clash against Manchester United next Sunday.
The 26-year-old added: "It was not the best circumstance but it was great to be back out on the pitch with the boys. At that point I came on, obviously you're trying to do your best and try to get something but it's also good to get back out there and back in the frame of playing again.
"It's been a very long and frustrating journey and although it's not the exact point I'd like to come back but it was good to be back out there.
"The fans were excellent. Even when we were behind, they were still singing. It goes to show why they are some of the best fans in the league. They will support us, no matter what is going on and we appreciate them staying behind us.
"I'm sure the fans are frustrated but we'll need all of them to be behind us. They are a tough team to play against. No game is easy in this league so I'm sure the boys will be ready and be sure to bounce back, showing the fighting spirit that we'll need to have and have shown for as long as I've been here."
