Tigers lost 15-9 at the Liberty Stadium, but the bonus point in defeat was enough to take top spot in Pool 3.
But Heineken man of the match Murphy said the moments just before half-time, with Tigers centre Toby Flood in the sin bin, proved crucial.
“That period was key,” said the Leicester Tigers full-back.
“It was a huge momentum-builder for us. With 14 men you are probably expected to give away some points and they had us under pressure, but we managed to hold out and they did not get anything.
“That was a confidence-builder for the second half.
“It feels a bit strange because we came here to win, we felt we could do that, and we feel disappointed that we did not do it. But credit to the Ospreys, they played it well and made it difficult for us.
“It’s disappointing not to win the game, but we have topped the group.”
A draw between Bath and Toulouse in Pool 5 on Sunday enabled Tigers to claim fourth spot in the list of qualifiers, claiming a home quarter-final against old rivals Bath on the weekend of April 10-12.
