Rumney's hopes of a Cup run were dashed at Laugharne on Saturday. Cooper's men travelled to the home of Dylan Thomas in a confident mood, but the writing was on the wall by halftime, with the visitors trailing 20-0.
Impressive winger Rhys Hallett inspired a second-half comeback with two tries, but Rumney are left to concentrate on the League after a 32-22 loss.
"We made a few changes to the side to rest a few bumps and bruises and we paid the price," Cooper said.
"We simply weren't clinical enough. We had as many chances as Laugharne in the first half, but they took theirs - we didn't. Fair play to them - they were a very committed side and they deserved the win.
"As the old cliché goes, we can concentrate on the League now."
Cooper said Saturday's trip to Tredegar - who are still looking for their first win of the season - was a must-win match.
"If we want to do anything in this League, we have to beat the sides in the relegation zone - if we don't, we'll join them down there. Having said that, the bottom sides in this League aren't as weak as they were last season.
"We did the job at Croesyceiliog (31-19) and we have to do it again at Tredegar. They're a tough side at home."
Rumney finished fifth in Division 2 East last season, and Cooper is looking for a similar placing this time around.
"We lost a couple of key players in the off-season, including our leading try-scorer Matthew MacLean, who went to UWIC. We've also lost a couple of tighthead props.
"Our lineout is going well - it's probably one of the best in the League - but teams will be targeting our scrum. We're working on that part of our game, but we're not the heaviest pack around.
"Our midfield are doing a lot of damage, and we've picked up a very good winger from Newbridge, Rhys Hallett. He's scoring for us most weeks, and they're good tries.
"If you look at things realistically, we'd have to be happy with about seventh in the table at the other end of the season. I'd be looking at finishing at least that high."
Seven of the 14 Division 2 East sides remain in the Cup. Table-toppers Pill Harriers beat Abergavenny 29-15, Llantwit Fardre trounced Llanelli Wanderers 46-7, Newport Saracens blanked Gowerton 36-0, Abercynon upset Division 1 club Waunarlwydd 41-37, Brynithel beat Tredegar Ironsides 44-22, Rhydyfelin beat Banwen 33-28 and Mountain Ash cruised home 54-24 against Caernarfon.