Shane Williams and Nikki Walker (thumb) found the Tigers defence difficult to penetrate
Ospreys coach Sean Holley described his side's 12-9 defeat at Welford Road as "a smash and grab raid gone missing".
Having held on by their fingernails in the first-half, the Ospreys got to within one score of victory in the second as James Hook added a penalty to Shane Williams' earlier drop goal.
Then came the defining moment of the game with the Ospreys being awarded a penalty at the foot of the home posts.
Ryan Jones ordered a scrum, but it was the Tigers who came up with the ball and cleared their lines to snuff out the match-losing threat.
"We let a real chance go begging in the end, but I'm still very proud of the players. They showed great character to hang in there right to the end," said Holley.
"It was a smash and grab raid gone missing. But we have the consolation of a losing bonus point and we are still right in this Pool and fighting.
"It is a measure of how far we have come as a team that a packed house at Welford Road, and all the Leicester Tigers players, were so happy with a 12-6 victory. We have come here in the past and been blown away in the second half, but I thought our tactical substitutions worked well for us this time and we were right in their fighting to the end.
"We need to be a bit more clinical and we need to learn from this game and improve before we meet Perpignan next weekend. But overall I'm quietly pleased."
The WRU has launched a campaign to create a long term legacy for Welsh club rugby by highlighting the advantages of volunteering. Rhian Edwards, a volunteer at Seven Sisters, has enjoyed many benefits of her volunteering at a grassroots rugby club including being part of the Rugby World Cup volunteer workforce after being nominated by the WRU - and the WRU is asking for more people to develop their 'Welsh rugby roots'.
Wales head coach Warren Gatland and captain Sam Warburton say their first prioirty on Sunday in the opening game of the World Cup is to win against Uruguay and not get overly concerned with points difference.
With only days to go until the biggest rugby competition in the world begins, rugby fans visiting Cardiff this autumn will be able to enjoy a special display at National Museum Cardiff as part of the celebrations surrounding the Rugby World Cup.