Rennie was speaking on the day the club's prize asset, Scotland lock Jonny Gray, had his move to Exeter Chiefs at the end of the season confirmed.
It will be a source of some consolation that the Warriors have secured the re-signing of Leone Nakarawa on a cut-price deal until the end of this campaign.
But Rennie - who hands over the reigns to current Scotland forwards coach Wilson when the former takes over as Australia coach this summer - believes it won’t be possible for Glasgow to spend their way out of a spell which has seen their best players - Finn Russell, Stuart Hogg and now Gray - seek pastures new and a drop-off in results.
"When you have top players, there is a lot of interest shown in them from big clubs in France and England," Rennie said.
“These guys [Russell, Hogg and Gray] have given their heart and soul to the club but now other teams have come in who can give them more than double what we pay them. It's a chance for these guys to set themselves up for life.
"The guys who have left here in the past have gone with our blessing.”
Gray has signed a two-year contract with English Premiership leaders Exeter and will be re-united with his Scotland team-mate and fellow 2015 Pro12 title winner Hogg at Sandy Park.
"I'm looking forward to the challenge," said the 25-year-old, 55-times capped second-row, who first signed with the Warriors in 2012. "I see the move not only as a chance to experience something new, but at the same time it's a chance for me to develop myself, not only as a player, but as a person.
“I know I still have a lot to learn as a player, so hopefully the change of club will allow me to add new things to my game.
"Leaving Glasgow will be tough. I love Glasgow and I'm so grateful to the club and so many people associated with the club for all they have done during my time there.
"Without doubt, this was one of the toughest decisions I've ever had to make - and I will be giving everything between now and the end of the season to ensure my time there finishes on a high.
"I've spoken to both Hoggy and Skins [Scotland forward Sam Skinner] and they've both said what a great club it is.”
Rennie reported that Fijian fans’ favourite Nakarawa, who was sacked by Racing 92 for arriving back late from the World Cup, is now in Glasgow after signing to the end of the season.
He won’t feature for the Warriors on Saturday as they look to get a faltering Guinness Pro14 campaign back on track against Benetton in Treviso and the Kiwi coach was unsure if the former European player of the year’s second stint at the club will extend beyond the end of the season.
"What we've got to understand is that Leone is a world-class player and there will be a lot of interest him - plus a massive price tag.
"That may well mean we can't compete with that. Our job is to make sure he enjoys his time here and hopefully that plays a part in his eventual decision.
"When you look at guys like Finn, Hoggy and Jonny, they were young men when they came here and over a number of years have developed into world-class players.
"We don't have enough money to go get someone of equal value because you are paying even more for them. It is what it is. We've got to find good young players and try to bring them through."