Talking in the Evening Times, Tyrone said: "Without our Scotland players we still believe we have the depth to cope. This is a great opportunity for guys who aren't playing in the Six Nations to put their hands up for a jersey and try and keep it for the rest of the season.
"We have two games in hand on all the teams above us in the Pro12 and if we win them we could go as high as second.
"It is vital we take care of business on Sunday. Our home form has not been as good as we would have liked, so we really need to make a statement against Connacht.
"There is an awful lot on the line this weekend."
The Connacht game comes off the back of Tyrone's first run out in Scotland A colours in the draw against England Saxons last weekend.
The 27-year-old flanker said: "It was fantastic to get my A cap against England Saxons at Scotstoun last Friday and that has given me a real boost.
"It was also good to get the game time and now I am officially Scotland-qualified, I just want to get out there and do my best for Glasgow.
"The A game has given me that extra bit of match preparation and sharpened me up for Connacht, if selected. We know this is our last home game for some time and it is vital we make the most of that.
"I played against Connacht in our first game and they are a tough, physically aggressive team.
"They play through the forwards and they will be full on, there is no question of that.
"I came off the bench for the first game over in Ireland and it was full-on stuff but I like my rugby that way. There can be no backward steps on Sunday."