Despite gaining their first point in that game, Ashley admits losing it has hit the Ospreys hard, especially given they had led for large parts of the game.
"It's incredibly frustrating to be in a game for 79, almost 80 minutes, and to lose it like that," said Ashley.
"We shouldn't have let ourselves be in that position going into the last minute. We can take a lot out of the performance considering where we'd come from in terms of improvements on the Ulster match, but we can't be satisfied with that.
"We have to be more disciplined, we need to be more clinical in key areas of the field. You have to get the basics right in order to see home tight matches like this from a winning position.
"The biggest pressure on us is the internal pressure we put on ourselves to perform every week and that is the same win, lose or draw.
"We'll review this, reflect on it, pick out the good and the bad, and go from there."
The result leaves the Ospreys sitting 11th in the GUINNESS PRO12 table, with only Italian side Zebre below them.
However, captain Ashley, who made his 50th appearance for Steve Tandy's side against Munster, is not worried about their poor start, as they prepare to bounce back against Edinburgh.
"As disappointed as we are at the moment it's definitely not time to panic," added Ashley.
"We know what we can do, we know what we are trying to do and we know what it takes to achieve that.
"We've got a few weeks to regroup now before we go to Edinburgh, to get things right. We want to get better as a squad and there is definitely an understanding that we have fallen short in the first two games but we are all working hard to improve.
"As a group, we know that we have to learn quickly. It was good to see that there have been improvements, and it was good to see people like Owen Watkin and Sam Underhill, both still teenagers and very raw, putting in such impressive debuts.
"The rest of us around them have to take some of the weight though. Young squad or not, there was enough experience in the 23.
"We won't hide behind 12 players on World Cup duty or injuries, we expect to miss players over the season and we all have a role to play if we are going to be successful."
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