Ter Stegen, 27, has been Barca's outright No.1 since Claudio Bravo moved to Manchester City in 2016, but has remained backup to Neuer in international football.
After being an unused substitute in games against the Netherlands and Northern Ireland during last week's international break, Ter Stegen revealed it had been a "massive blow" not to feature at all.
Neuer responded by saying his comments were not helpful. The Bayern Munich stopper added that Ter Stegen didn't say anything while with the German camp and suggested he was also being disrespectful to the other goalkeepers pushing for a spot -- naming Arsenal's Bernd Leno and Eintracht Frankfurt's Kevin Trapp.
"There's competition for places and every player wants to play," Ter Stegen said in a news conference ahead of Tuesday's Champions League game against Borussia Dortmund in his homeland.
"That's football. A lot of the time you're happy, but there are also other feelings. I have expectations and I have to express them.
"You can see how I have behaved in recent years and I don't think that Neuer or others have to talk about my feeling or assess them. His remarks were inappropriate but I don't want to say much more, I want to bring an end to all this controversy."
Ter Stegen has won 22 caps for his country but has played just once during 2019 despite being promised action in the qualifying campaign for Euro 2020 by coach Joachim Low. That one appearance came in a friendly against Serbia, in which he played 45 minutes.
However, he remains Barca's first pick and will start on Tuesday back in Germany when the Spanish champions face Borussia Dortmund -- coached by his former manager, Lucien Favre -- in the Champions League.
Barcelona's defence is under the microscope, though, having conceded seven goals in just four league games this season.
"We're trying to stop the goals going in but things haven't come off," Ter Stegen said. "It's not what we expected. We have to improve. There have been mistakes which we can easily correct. We've spoken about it."
The game at Signal Iduna Park signals the start of a new European campaign for Barca as they look to get over last season's semifinal loss to Liverpool and win the Champions League for the first time since 2015.
"We know that we have to fight for everything every year," Ter Stegen said. "One defeat against Liverpool complicated our whole season last time out. But we have a team to be convinced that we can have success.
"Winning the Champions League is always our objective. Last year we messed up at a key moment."