Following a surprise 12-6 defeat to Treviso, the Ospreys were beaten 13-16 by Ulster at the Liberty Stadium despite a try from Hanno Dirksen. And Tandy knows his side must improve, starting with the game against the Warriors.
"We are well aware that we need to improve from where we've been over the last two weeks but we also know where we are in terms of a long season," he said.
"We've been able to change things about to give some more boys a chance, but we've selected a team good enough to do the job, just as was the case in the last two games.
"Obviously we've been hugely disappointed by how things have gone but the finger isn't hovering over the panic button. We've reviewed Saturday's game and what went right and wrong on the night. We aren't that far away from where we want to be but in reality we need big improvements in application, discipline and accuracy if we are going to turn possession and chances into wins.
"We need to get back to what we were doing at the end of last season, playing mature, intelligent rugby that allowed us to go through the phases and really make it count."
Grabham takes his place on the wing while Welsh lock Alun Wyn Jones drops to the bench. Ryan Jones, Tom Habberfield, Tom Isaacs and Jonathan Thomas are among eight players out injured.
Like the Ospreys, Glasgow are also yet to register a victory following two successive defeats. The Warriors lost 18-10 away to Ulster on the opening weekend of the season before the Scarlets triumphed 18-13 in Scotland last Friday.
"This is an important game for us, against a very good, very powerful and very dangerous Glasgow team," Tandy added.
"Like us they'll be disappointed at the start they've had, but we know they are a real threat. They were in the PRO12 semis last season, as they were two years ago, and just as we haven't become a bad team on the back of two defeats neither have they.
"Hopefully there'll be another big crowd there. The support last Saturday was great and we need the same again to lift the boys and really help them across the line. The difference the supporters can make is huge."
Ospreys: 15 Richard Fussell 14 Hanno Dirksen 13 Jonathan Spratt12 Ashley Beck 11 Tom Grabham 10 Dan Biggar 9 Rhys Webb, 1 Duncan Jones 2 Richard Hibbard 3 Aaron Jarvis 4 Ian Gough 5 Ian Evans 6 George Stowers 7 Justin Tipuric (c) 8 Joe Bearman.
Replacements: Scott Baldwin, Ryan Bevington, Joe Rees, Alun Wyn Jones, Sam Lewis, Kahn Fotuali'I, Matthew Morgan, Andrew Bishop