Although the Whites were unable to turn consecutive victories into three straight wins despite taking the lead through Jack Harrison, new coach Marsch is trying to focus on the bigger picture, and was pleased with what he saw from his side in a game that was at times extremely frantic.
Harrison's goal was cancelled out by a second-half free-kick by James Ward-Prowse and despite a number of chances, Leeds were unable to find a winner. Their coach, though, was pleased with the performance.
"There was a clarity of what we want the game to look like tactically, we were balanced, we didn’t give much away," he reflected. "We are trying to turn advantages into real chances, real chances into goals.
"I’m not worried about that - we have quality, with this style we will always be able to create chances. If we could just slow down and make the last pass a little cleaner or crisper then we’d have more goals. We’ll keep working on it but it’s a step in the right direction.
"We tried to organise ourselves to defend better in all phases, including set pieces. The lads are intelligent, they adapt well.
"We had a little bit more time with 75 per cent of the group (during the international break) to work through tactically what we want games to look like.
"I did less shouting to the players this match because they were more in control of every situation."
Both managers, who know each other well from having worked in the global Red Bull network - Southampton's Ralph Hasenhuttl for Leipzig, Marsch for the German side, Salzburg and New York - claimed the match had panned out as they expected, and that their team ought to have won, although the Leeds manager back-tracked a touch later to admit a draw was a fair result.
"It was an intensive game with a lot of second balls and duels, one that we should have won," he said. "We knew it would be like this - intense, tight, important to try, in compact moments, to find forward solutions to get into transition moments and put pressure on opponents.
"Any time Southampton get in your half, they start throwing balls into the box. (Ward-)Prowse has incredible service, feeling the pressure. We stood up to those moments well.
"The foul (by Luke Ayling) leads to what I call a penalty - Prowse is so effective from direct kicks. We knew it would be important not to give fouls away. He put it right in the corner like we were worried he might."
His Austrian counterpart reflected: "I think it was the expected game. I spoke before the game that it would be like ping pong, two teams who like to play quick forward.
"We tried to avoid playing in our own half, we knew the pressing would be intense, we wouldn't have much time (on the ball).
"Their behaviour is similar to ours. We had more chances, the better ones, we had been closer to win this game. We take the point, it's a good step forward in an intense atmosphere and game. To go away with a point is okay."
Joe Gelhardt made an impact from the bench, as did Kalvin Phillips because Liam Cooper started. Marsch had said beforehand both senior players were able to start but unlikely to finish the game, so only one was likely to do so. Cooper played the whole 90 minutes but only because of an error by the Leeds bench which saw Ayling brought off instead.
Cooper was selected ahead of Pascal Struijk, Ayling's replacement from the bench.
Marsch explained Gelhardt and Struijk's reduced roles were the knock-on effects of a Covid-19 outbreak at Thorp Arch during the international break.
"Pascal was positive in the break and coming back out of Covid, he picked up a little hamstring injury so he didn’t train fully," he explained. "Cooper had. He looked strong and good and clear, it was a relatively easy decision to make given circumstances.
"I was concerned whether Coops could make 90 minutes. Given the way it went, it was good he was able to play a full match.
"There was a mix-up with staff. Luke had a little situation where he had to come out for a second. Liam was feeling heavy, we wanted to get him out of the game and put Pascal in at centre-back. Clearly the communication wasn’t what it needed to be.
"One reason why Joffy (Gelhardt) didn’t start was because he tested positive at one point during the week, a false positive, but he missed a day and a half of training. It was a bit of a strange situation.
"We haven't been able to get him going, with rhythm in training. He is playing more of a reserve role.
"He gave us a boost (when he came on) - he is clear with the role, dangerous at times. I am considering expanding his role more and more within the team.
"The plan is to play him with the under-23s on Monday, get him more game minutes and adapting."
Leeds are now eight points ahead of the relegation zone and Watford, who have a game in hand and host the Whites next Saturday. Leeds are unbeaten in their last three matches.
"The points are always important," commented Marsch. "The focus is so much on work, progression, development, commitment, we have quality to manage the moment, push it in the right way.
"I go to say good game to the players and the opponents and everyone is looking to the board to see what the results are. That's the reality of the situation. We are tying to keep focussed on the work."