With several key men missing, it was a tough evening for the visitors, who succumbed to two first-half goals in Germany and lost Jozo Simunovic late in the game, a setback that leaves them with a defensive crisis on their hands.
The result lifts second-placed Leipzig three points clear of Celtic in Group B after three matches, while Salzburg are a further three points ahead of the German club following their 3-0 victory over Rosenborg on Thursday.
But Hoops boss Rodgers said: "There were a lot of positives from the game".
"We always knew our home games would be vital for us and try to pick up something away".
Red Bull Leipzig manager Ralf Rangnick has hailed the talents of Celtic wonderkid Kieran Tierney, as well as his team-mates Callum McGregor and Odsonne Edouard.
However, numerous supporters took to Twitter to slam the vast majority of the side that played, with one man, in particular, receiving plenty of criticism. "We have to look to win next time and, if we don't, it is really hard". We trust in everybody in our squad and we're looking forward to this game.
Obama, Clintons sent 'explosive devices' through the mail
In a statement , Press Secretary Sarah Sanders denounced the threatening stunts, saying "these terrorizing acts" are despicable. In addition, CNN's New York City studio was evacuated Wednesday morning due to a suspicious package being found.
Owner claims dog is 'gold diggin' pretending to be stray for McDonald's
Reyes wrote that Princess "doesn't know how to act" and has been taking unapproved night time strolls to the fast food restaurant. Reyes' shaming of her dog has been liked over 290,000 times on Facebook and has been shared almost 275,000 times.
China blasts Trump phone hack report as 'fake news'
It's alleged that China is taking note of who Trump speaks to most frequently, so he can be targeted with pro-Chinese messages. Over the summer, President Trump officially banned all government use of Huawei products.
"I felt we were finding the spaces well and getting in good positions".
"And we had a period of 15 minutes after that when we made a mistake from a cross coming in and at this level you get punished for that. I believe it gives us a great chance but we know we have some work to do".
Rodgers told "BBC Scotland", "We're still in with a great chance".
Celtic possess some of the most passionate fans in the world, and this entertaining video just shows them at their best, as they are all behaving a terrific manner and are all just enjoying supporting their club on foreign soil, so they must be commended.
'Unfortunately Dedryck Boyata, who I thought was outstanding for us tonight, won't be available at the weekend for us.
"They don't play typically kick and rush of Scottish football".