Reus' second-half goal set Dortmund on their way to a comfortable cup victory on Friday, just a week after they beat Bayern Munich 2-0 in the German Supercup.
"The two wins were important for us to find our rhythm," Reus told Sport1.
"We are not yet quite at the level that we were at last season, but we have big plans this year, and we want to show that when the Bundesliga starts next weekend."
Dortmund, who host Augsburg in their Bundesliga opener next Saturday, were forced to be patient against a well-organised Uerdingen defence which included former Dortmund fan favourite Kevin Grosskreutz.
Grosskreutz, a World Cup winner in 2014 and two-time Bundesliga winner with Dortmund, denied his old team early on with a goalline clearance.
The underdogs then gave Dortmund a scare at the other end shortly before half-time.
English striker Osayamen Osawe skewed a shot wide after pouncing on a mistake by Mats Hummels, who was making his first appearance for Dortmund since returning from Bayern Munich in June.
Unfazed, Dortmund took the lead just after half-time, Reus flicking in Manuel Akanji's long ball as the Uerdingen defence came fully undone for the first time.
With 20 minutes to play, Alcacer put the game beyond reach with a brilliant direct free-kick.
Elsewhere on Friday, Nikola Dovedan's 87th-minute winner fired second-tier Nuremberg to a 1-0 victory over third-division Ingolstadt.
Reigning league and cup champions Bayern travel to Energie Cottbus for their first-round tie on Monday.