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 cut 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 them, starting with in-form Motherwell on Saturday.
Draper is confident they can handle the pressure of the three-horse race for Europe and 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.
"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."