But while the win moved Glasgow above Ospreys into second and all-but sealed their place in the playoffs, Lineen is adamant he expects more from his players in their final league match at Scarlets.
"To get the win was fantastic," said Lineen. "Leinster don't often lose by that amount of points but I'm disappointed not to get the bonus point.
"The win was always what we concentrated on, but for large periods of the game we couldn't get our attack going; they slowed the game down and we lost our composure at times.
"We've got to win away at Scarlets now and make sure the players have the right mind-set."