Dase said that his team could have put the Knights away earlier.
"I am disapointed," he said. "They were on a cliff, and we never kicked them off the cliff. We had two goals. It should have been three or four. We don't put them away and that's been a problem with the team all year."
Fifth-seeded Towson (5-7-1) will advance to play top-seeded and host Woodlawn Tuesday in a section semifinal.
Goals from senior forwards Austin Tippett and Titus Sparshatt made that possible.
The Generals put a bundle of pressure on goalie Timothy Miller (8 saves) and the defense of James Reardon, Ross Boyer and Mario Colandrea right away.
The Knights survived it until Tippett scored in the 17th minute from 16 yards out. It was his second goal of the year.
Towson junior goalie Christian Sorteberg kept it 1-0 game with a diving save about a minute later on Kyle Genung's blistering shot.
"The play of the day was by our goalkeeper," Dase said. "We are up 1-0 and he makes an unbelievable save. If it was 1-1, it would have been a war. That was the key to the game."
Towson had some excellent scoring chance late in the half, but Miller saved a point-blank shot from Noah St. John and Nick Hayden hit the post.
The Generals' second goal was especially impressive. Sparshatt kicked a left-footed shot to the upper right corner early in the second half on a crossing pass from Hayden.
"We know they play quickly and with a lot of pressure," said Parkville coach Gary Burkhardt, whose team lost to Towson, 3-0, in the regular season. "We expected some quality footwork up top.
"Towson has that desire to win the ball," he added. "There's 50/50 challenges and some could have easily been ours. They did a better job of winning those situations."