Warriors sent seven tries in their 56-27 defeat Allianz Park, their 3rd loss to Saracens this season.
Rennie bemoaned his side’s errors as these were put into the sword.
“once you get to the significant occasion, you need to front and work a lot better than we did,” Rennie told BBC Scotland.
“We needed everybody to be on song but we made way too many errors, particularly kicking errors. We got dominated field position-wise and [there were] too many soft defensive attempts”
Glasgow made an ideal start when scrum-half Ali Price scored after two minutes, but Saracens responded almost immediately through Wales international Liam Williams and never looked backagain.
“I thought we defended well right after [Cost’s take to ] and we now got a turnover – and then Adam [Hastings] withdrew an apology which ended up down our end of this field and so they felt long later,” Rennie said.
“You can not offer a great side like Saracens chances – and that we gave them a lot”
Having come away with a narrow 13-3 loss at the very first meeting with Saracens in 2013 at Scotstoun, Glasgow have surrendered 94 points on their past two visits into Allianz Park.
Lock Scott Cummings went off with a head injury in the first half and fellow second-row Tim Swinson was stretchered off with an ankle problem, which Rennie says”doesn’t look too good”.
They have three regular season matches left at the Pro14 and sit top of Contest A, with Ulster up alongside Scotstoun on Friday.