Heung-Min Son's 62nd-minute strike from distance gave Leverkusen an important three points, seeing them stay unbeaten in league games at Gladbach since February 1989.
The victory lifted Leverkusen seven points clear of second-placed Borussia Dortmund, who face Werder Bremen on Saturday, while Gladbach sit fifth in the Bundesliga.
Favre said rushing their play cost his side in the second half and felt that was the difference between the teams.
"I think the first half wasn't spectacular but it wasn't bad. We played with a lot of patience, possession was OK. We lost the ball too often. The way we got it back was good," he said.
"In the second half we simply lost patience. Instead of keeping it simple and switching sides we lost the ball too often which was unnecessary.
"Obviously Leverkusen does well in getting the ball back.
"They are extremely dangerous on counter-attacks and in this case we had lost a ball that we should have played over the wings but instead our thought process behind our defensive and offensive positions weren't good."
The loss extended Gladbach's poor form in the league this year, with the defeat marking their third straight in 2014.
Favre said a concentration lapse was costly for the goal, with his team not in the positions they needed to be to defend.
"I always say that when a good team is attacking, it needs to have thoughts about what to do in case the ball gets lost," he said.
"And in reverse, if we are defending we need to already have thoughts about how to attack with the ball when we get it back. That's what makes up a good team.
"In the phase where we conceded we forgot about that shortly and against such a team like Leverkusen that counters well that's bad.
"I find it a shame that we lost patience instead of trying to move the ball across and try to get the other team a little tired even though they run a lot.
"Well, those details were important for me and that's what made the difference."
