Scotland lock Gray will join Sharks on a three-year contract as the Warriors failed in their bid to retain the services of the 22-year-old, who scored a dramatic added-time try in their 26-21 Heineken Cup defeat of Bath on Sunday.
Rated as one of the most exciting talents in world rugby, Gray played in all of Scotland's World Cup games, taking his tally of international caps to 16.
But now the 6ft 8in lock has announced his departure, Lineen admits they need to fight harder to keep their best players if they are to compete in the RaboDirect PRO12.
He said: "We have signed five young players [this season]. We are ambitious, we want to do well, and we want to win things.
"We want to keep our young players instead of losing them every year, which is what we tend to do at Glasgow especially.
"It is part of the game and we do lose players, but not without a fight. In the past maybe we haven't really fought hard enough or had the clout.
"When you look at the Lamont brothers, Euan Murray, Dan Parks, all these guys have moved on but we want to keep these guys."
Gray, who was reportedly courted by Bath, Saracens as well as some French sides, follows countrymen Fraser McKenzie, Richie Vernon and Alasdair Dickinson at Sale.
But Lineen is adamant the next generation of talent coming through at Firhill can fill the void and become the basis of the Warriors team for years to come.
"We have lost eight or nine players in the last three or four years so it will be key to us moving forward to keep them," he added.
"The first stage is to keep these players and get a settled team, and to be ambitious and challenge for things.
"The young lads have really stepped up. I have integrated them since the World Cup. We played a few of them against the Ospreys [28-17 win last month].
"The young captain who replaced Al [Kellock] during the World Cup, Rob Harley, and he has done outstandingly well. He is only 20-years-old and he has the led the team very well.
"You create that depth and competition which all the top teams have, and that is what you want so it makes it difficult for them all to play.
"We had three wins in the Heineken Cup last year. If you look at the financial table we are not near the top.
"We just need to get that consistency and keep the momentum up. We have had one or two big results but then faded away.
"We want to make sure we can compete and win. That is what it is all about."
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