Not really.
Our fans don't listen to Pep enough. Rivalry is not only about the final result, but also about the quality of performance. You can't control the result at 100 %, for luck plays a significant role in a low-scoring game like football. No matter how we play, the opposition always stands a chance to win/draw, especially if it's one of the best teams in the world.
Clearly, Pep was happier than Klopp after the game. Why? For two reasons: the draw left us in the driving seat, and we outperformed them. The latter was very important to Pep and the players.
Given that football involves chance, performances are the best predictor for success. You can luck your way to some wins or even trophies, but the quality of performances is the most solid basis for winning big trophies.
One of the main mistakes many posters make on football forums is that their perspective on the game is often distorted by the result at the expense of the performance. Had Mahrez scored that chance, the thread would have been completely different, and the performance would have been lauded as one of the greatest ever.
We'll play worse in some big games over the next weeks, but will score more goals and win. We played much worse at Sporting but won 5:0. That's football.