The stalemate at St Mary's, only the fourth time this season the Reds have not won, saw them lose top spot after just one match as Premier League leaders.
Klopp felt that after scoring 10 in their previous two games against Crystal Palace and Watford prior to the international break there was a growing belief outside of their Melwood training ground bubble that his side would continue to fly through fixtures against the so-called lesser sides.
"The Southampton game was really important for us - the result was not too nice - but the games before looked a little bit like we were in the flow and it was easy," he said.
"Then we had this day when we didn't score early - didn't score at all - but we stayed in the game and we are ready for the work we have to do.
"Not at the 12th match day (can you) have expectations about the games because we are in a good position.
"If someone was disappointed after the game we were not first in the table any more it is really crazy.
"If you want to keep this position or make it better you have to improve 100 per cent and there is a lot of space for us.
"If I had any doubt about the attitude of the players it (the Southampton result) would have helped because with 80 per cent concentration you get nowhere in the Premier League.
"But it wasn't about attitude so I was really happy with the attitude and a lot of parts of the performance."