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."
Carmarthen Quins are holding an exhibition to commemorate club players who fought in World War I. All welcome to the clubhouse on Friday afternoon to learn more about local history, or share any family anecdotes or artifacts.
Defence coach Shaun Edwards believes Saturday's clash against England - the 'form team in world rugby' - poses a huge challenge for his side but he is confident, with Wales beginning to show the defensive qualities displayed in the last two World Cups,
Women in the Ospreys region recently completed a Level 1 coaching course and are looking forward to putting their theory into practice in clubs and schools across the region. A women only course has been organised for the Scarlets region starting next week, full details at the end of the video.