The Sounders were beaten 1-0 at home by the Mexican side last week and fell a further goal behind when Carlos Quintero struck in the 21st minute in Torreon on Tuesday night.
Seattle struck back through Lamar Neagle with just over 15 minutes remaining but in the end could not get the job done as Santos progressed to the final where they await reigning champions Monterrey or LA Galaxy.
Schmid was happy with the character shown by his players but rued the fact they could not come up with a winning scoreline.
"We put ourselves in a position to advance, which was also very good. I think the character that we showed tonight and that we played with, being down at halftime 1-0 was no different than our situation was against Tigres (last season)," he said.
"We knew we needed to score just two goals to advance, not three, and the guys battled. We put ourselves in a position where we could have advanced and won it. Our finishing needed to be better, but I'm proud of our quality and the effort we put in tonight.
"It shows that we have character. It shows that we've closed the gap."