Glasgow sit top of the PRO12 a point ahead of Ulster with just three games of the regulation season left.
Glasgow face the Scarlets tonight followed by a game at home to play-off chasing Ospreys and a tough trip to Galway to face Connacht.
Peter told the Evening Times: "Our form of late has been very consistent, our only defeat in the last nine PRO12 games came at Leinster when the ref called my pass forward at the death and we missed out on a match-winning try.
"But at the same time, we know our high standards that we have set ourselves in these games can't fall away. Scarlets came to Scotstoun in the second game of the league season and we didn't get to grips with them at the breakdown.
"To be honest, we were on the back foot for the full game.
"With the likes of winger George North coming on to quality ball, you are always going to be under pressure.
"So we know that we must get off to a very positive and solid start and really try and take the fire out of their bellies."