England's win over South Africa on Sunday secured the Twenty20 series.
The game was officially sold out, as were England's two ICC Champions Trophy matches at the SSE Swalec Stadium.
The near-15,000 crowd comes as counties bid for the next round of five years' worth of international games.
"To have three full houses over 19 days for England matches is something we've very proud of," said Morris.
Cardiff hosted England's win over New Zealand and semi-final defeat to Pakistan in the Champions Trophy, along with Sri Lanka versus Pakistan and the less well-attended Bangladesh v New Zealand match.
Around 3,000 seats were not occupied for the England v New Zealand match because of poor weather forecasts, while cancelled trains are believed to have contributed to some empty seats for the T20 on Sunday.
But a rapid re-allocation of tickets worked well for the England-Pakistan game after fears that India supporters, who bought tickets for both semi-finals, would not turn up.
"It's particularly important (to have big crowds) this year, because at the back end of the year we are likely along with other counties to be bidding for our international programme between the years 2020 and 2024," explained Morris.
"There's also the new city-based franchise T20 as well, so it's important we can demonstrate we can fill houses and people have a great time when they are here."
England's score of 181 in 20 overs against South Africa could also come as a relief, after captain Eoin Morgan criticised the use of a previously-used wicket for the Champions Trophy semi-final, a choice attributed to the International Cricket Council.
"I wasn't surprised (with the score), it's a wicket that has played extremely well this year in domestic and international cricket, in recent years we've had some very good marks," said former county captain and England opener Morris.
Glamorgan have forecast an operating profit for 2017 on the back of five days of international cricket.
But it appears unlikely they will add another overseas player to their squad for the T20 Blast, after signing South African paceman Marchant de Lange on a three-year deal for all forms of cricket.
Glamorgan chief executive Hugh Morris says Cardiff's third sell-out for an England match in June will boost their hopes of attracting further international matches.