Caley Thistle head the way to join Motherwell and William Hill Scottish Cup finalists Hibernian in the Europa League but their lead in the race for third was cut to one point when they fell to a 1-0 defeat at St Johnstone last weekend. Ross County's victory over Dundee United the previous night had closed the gap to two points and Inverness face their Highland rivals on the final day of the Clydesdale Bank Premier League season.
Caley Thistle have two home games before then, starting with in-form Motherwell on Saturday and Draper said: "We knew at the split we had five tough games. We knew it wasn't going to be decided over the first two games when we know going to Celtic is tough and St Johnstone are doing well at the moment."
He added: "We saw the next three games as the games we were expecting to pick points up. We are not panicking that the others have closed the gap.
"Everyone has to play each other and I think you will see in the next few weeks hopefully we can pick up some points and increase that gap.
"We have got three games where we don't have to travel. We know we can match anyone at home. We back ourselves to get over that finishing line and finish the season off as what we deserve, really."
Caley Thistle have taken points against every team but Motherwell this season and their games against the Lanarkshire side have been the difference between the teams in the league.
Motherwell lead Inverness by nine points and 12 goals - the same number they have put past Terry Butcher's side in three matches.
Draper said: "They are a terrific side but for some reason they have done especially well against us.
"It's a game we need a lot of preparation for. We have been planning to stop that and see where their main threat is and where we have gone wrong in recent games. We know we have to be on our game and put them under pressure to get anything."