The Welsh region overcame the Cherry and Whites two tries to one - scored by centre Steffan Hughes and wing Aaron Warren - in a closely fought encounter at Parc y Scarlets, leaving Easterby satisfied with the position his team find themselves in.
"We have given ourselves a chance of qualifying for the knockout stages," he said.
"Northampton have to play the at Newport Gwent Dragons (on Saturday) and after that it could come down to how we get on at London Irish next week.
"I was pleased with certain aspects of our play, but the defences were more on top and it was not a night for attacking rugby.
"There were some good individual performances and I was pleased with the result.
"We felt comfortable without the ball. We got lucky with the first try and the second one came from a turnover. It wasn't a great night for rugby."
Easterby added: "We needed to give a lot of people game time, and we achieved that. I was pleased with the overall work-rate and application, although the conditions were never going to be good for rugby."
Gloucester forwards coach Andrew Stanley was happy with how such a young visiting side fronted up at Parc y Scarlets.
"We were disappointed we didn't get the result, but as far as the performance was concerned we came over to Wales with an inexperienced side," he said.
"We had three players out there who are in our under-18s programme and they had to get time off school to train this week. One had to be pulled out quite late because he was behind with his maths.
"I spoke to a couple of the youngsters afterwards and they said they had never come across anything of that physicality or speed before, which is understandable."
- Sports & Recreation
- Parc y Scarlets
- Newport Gwent Dragons
- Steffan Hughes