Ryan told the Evening Times: "Our backs are against the wall but we are a good side and we are 100% determined to prove that the Scarlets game was just a bad day at the office.
"Ospreys are the defending champions and they will be coming here determined to keep their own fine form going.
"But we know that with the extra stand going up we could have a new record crowd of 9,000 at Scotstoun for us.
"We realise that we need to produce a response. We have been very consistent over the second-half of the season and the Scarlets game has been the only time we dipped below the high standards we have set ourselves."
Warriors will host Ospreys and then head to Connacht for their final game of the regular season while leaders Ulster have ties away at Connacht and then at home to the Blues. Second-placed Leinster – who are just a point better off than Glasgow – will face Ospreys at the RDS on the final day of the regulation season, in a game both sides will have to win.
Ryan said: "We want to become the first Scottish team to win this title. That has always been the goal.
"The Heineken Cup was a big disappointment for us this season and we have been determined ever since we went out of it to take our challenge in the PRO12 all the way.
"There are two games left to play and we know that if we can win them both, we can hopefully still claim the home play-off semi-final we have not achieved before.
"The last time we lost to Scarlets we went to the Liberty Stadium and turned over Ospreys, so hopefully we can repeat that.
"It's up to us, we know what is required and we know we will have to dig deep, but at Scotstoun we fancy our chances against anyone with our fans behind us."