Marius Bulter scored twice as Union broke their top-flight duck with a shock 3-1 win over last term's runners-up.
Bulter's first-half strike was quickly cancelled out by Paco Alcacer, but the former scored again five minutes after the interval and Sebastian Andersson then added a third for the Bundesliga new boys.
"I think we thought it would be like the second half in Cologne. That was not the case," said Dortmund head coach Favre, referencing last Friday's match in which his side trailed 1-0 at the interval but triumphed courtesy of three goals in the final 20 minutes.
"We have to keep our patience and not play hastily with the score at 1-1; we have to defend very well. This is very important.
"Instead, we have lost our patience [and conceded] an unnecessary goal.
"Even then, we should have kept patient. There was still time to make it 2-2 and maybe win the game as well. Our second half was not good."
Dortmund had taken an early lead in the race for the title, capitalising on an uncharacteristic slip-up by champions Bayern Munich on the first day of the season.
The Bavarian giants drew their opening game 2-2 with Hertha Berlin and Favre’s side were able to win their first two games.
Having lost last season’s championship by just two points Dortmund will know each win is vital as they look to end Bayern’s stranglehold on the league crown.
Bayern have brought seven straight titles to Munich and smashed Mainz 6-1 before Dortmund kicked off on Sunday.
Union Berlin were promoted to the Bundesliga for the first time at the end of last season. They have been a club since 1906, and have played under their current name since 1966.
German domestic football will shut down for the next two weeks as the clubs take in an international break.