The Murrayfield triumph ended a five-match losing streak and was Scrivener's first since taking over the reigns from Rob Moffatt on January 31.
"I'm really proud of the effort from the boys. It's been a tough period for us but I just thought that if we kept working hard and kept our heads down, we'd come out the other side," Scrivener told Edinburgh's official team radio station.
"I'm pleased that our guys got their rewards for their perseverance over a difficult period.
"We needed a 'w' next to us desperately. It makes a massive difference. It was a happy changing room and it hasn't been a happy changing room for a while."
Edinburgh scored two tries against their high-flying Welsh visitors to bring the Ospreys' seven-game winning sequence to an abrupt end.
Wing Tim Visser and full back Jim Thompson both crossed the whitewash as the Scottish capital outfit produced an entertaining brand of rugby.
"The things that we've been doing well in other games but not for long enough we did for longer," added Scrivener.
"We got our shape and we actually played some good rugby. We used the ball well and scored some good tries, and they're the things we've been practicing.
"It's pleasing that we got back to playing Edinburgh-type rugby."
Edinburgh currently sit in ninth place in the standings but seventh place seems a realistic target with a decent end to the season.
Scrivener's men now have four games remaining and each of those matches is against teams in the bottom half of the table.
First up is a trip to Connacht, who are just a point above Edinburgh in eighth spot.
Then comes a home clash with bottom-placed Aironi before the Dragons are welcomed to Murrayfield in Round 21.
Like Connacht, the Dragons are just a point ahead of Edinburgh, while their final day opponents, Treviso, are three points further back.
But while Saturday's win was exactly what Edinburgh needed ahead of the run-in, Scrivener admits there is still plenty of work to be done if his side are to climb the Magners League ladder.
"We're still where we are in the table. It's given us a lot of heart, though, for what we're doing and where we're trying to take the team. It's good to get some reward for some of that effort.
"We know the problems that an away game at Connacht has posed everyone in the competition this year. They turned us over in the corresponding fixture last year, so we're under no illusions as to where we're at as a rugby side and the challenge we face next week."
63x46.png){kind=logo}