A seven-wicket victory over Middlesex sealed Glamorgan's place at the top of the Southern Group and a home tie with Leicestershire in the last eight.
"It would be a great achievement, it's really important to perform well in the quarter-final," Morris said.
Glamorgan will try to secure the return of batsman David Miller for the match.
The South African left-hander, who was contracted to Glamorgan for six group games, is due to be playing for South Africa 'A' in Bloemfontein until the day before the Cardiff quarter-final on Wednesday, 23 August.
"It's going to be very tight, no question, but if David's here it's a bonus, if he's not, we still believe we've got a squad to perform well since we've won a lot of games without David," Morris told BBC Wales Sport.
Glamorgan have only previously reached Finals Day once, ending in a semi-final defeat against Leicestershire in 2004, while they lost in the quarter-finals in 2008, 2014, and 2016.
Coach Robert Croft was pleased to end the home campaign with a win in Cardiff, albeit again shortened by rain, after four wash-outs and two defeats.
"The supporters that have been here all summer, shall we call it a summer? It's been important we got a game on and showed people what we could do, we played very well," he said.
Glamorgan chief executive Hugh Morris says it would be a "great achievement" for the club to make T20 Blast Finals Day for the first time since 2004.