Peel says confidence is growing in the squad as they continue their United Rugby Championship campaign.
"One of the things we are trying to do which we weren't able to do last season is playing at a higher level and higher intensity so we can compete longer and against the top teams," Peel said.
"I firmly believe we turned the corner in that regard; there's a belief within the squad that they can do that.
"They've gotten there a few times in the earlier games that we've had.
"We know the physical markers are way above where it's been previously. Just the belief and confidence in the group is growing."
That mindset was put to the test against the Stormers, with Peel stressing the need to confront rather than admire the Cape Town side's style of play.
"We spoke about it; one can't come here and admire how the Stormers play," he explained. "We had to come here and challenge them and dare to be great.
"That was the message really; we've got to pitch up and go after the Stormers, with or without the ball, and I felt we did that for long periods.
"Even at half-time when we were a little bit under the pump, we still spoke about going after half-chances and using those opportunities, and the guys came out and played some great rugby in the second half."
Physicality remains a non-negotiable against South African teams, and Peel felt Scarlets met that challenge for large stretches of the contest.
"The one thing you're going to get from South African teams is physicality; the boys spoke about it all week, and I felt we did that for large parts of the match," he said.
"We felt that if we could physically match that intensity, we knew we had enough rugby in us to cause some problems.
"Those two elements came together, and I'm extremely proud of what we were able to produce today [Saturday], albeit being disappointed in the fact that I feel there was more in it for us. We go in positively to the next challenge [Bulls], which is not going to be easy."