After missing most of the first half of the season to injury, Koch played every minute as the Whites claimed back-to-back league wins for the first time this season.
As well as positive recovery milestones for Koch, the two results put daylight between Marcelo Bielsa's side and the dreaded dotted line as the Whites moved up to 15th in the Premier League rankings.
With 18 games left to play, United are far from home and dry, but ahead of Saturday's Premier League game against relegation-threatened Newcastle United, Koch said he is unconcerned by the risk of dropping out of the top flight.
"For me, personally I don’t fear relegation - I’m looking forward," Koch said.
"I’ll be confident and positive enough to say that we don’t go down and we will get enough points to stay in the league and I think the same for the whole team.
"I think that we should focus on getting out of the lower part of the table.
"We did well with the two wins now in the league, but this has to be the start and we have to keep going so we’ll see how we end the season."
The German is finally making strides in Bielsa's team; this January, Koch started two consecutive Premier League games for the first time since May 2021.
Following his arrival at Elland Road in August 2020, Koch's first season was disrupted by a knee injury and this term the 25-year-old featured in just one game, the Whites' 5-1 thrashing at Old Trafford on the opening day, before a pubic bone contusion put Koch out of action for several months.
The defender, though, applied the same positivity to the relegation threat and his long-term lay-off.
"I think it's just part of my personality, I try to focus on my comeback," Koch told the BBC.
"I’ve been in contact with lots of friends during this time and my family.
"It's not always possible to get them over, but to speak to those people is also an important thing.
"Even during my injury, I try to stay positive every day.
"Of course for every player it's not easy to get a long term injury.
"It wasn't the easiest time, but I tried to be positive during this time, imagining my comeback and working hard every day for it.
"I’m really happy to be in this position now and happy to play again."