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."
GB7s women left their England base to train in Wales this week. Olympic Games hopeful Rachael Burford gives WRU TV's Graeme Gillespie her thoughts on Welsh teammate Jasmine Joyce - a 'one touch wonder'
The GB7s women's squad is currently training at Wales' Centre of Excellence where assistant coach Richie Pugh tells WRU TV's Graeme Gillespie some 'tough calls' will have to be made when it comes to finalising the 12 spots for Rio's Olympic Games.
Wales U20's Billy McBryde is looking forward to starting his first game against New Zealand this afternoon in the World Rugby U20 Championship where his side are looking to gain revenge from last week's pool defeat to the Kiwis.