Caley Thistle lost three games in eight days - including two cup ties against Hearts and Kilmarnock - before turning their attentions to tomorrow's visit of SPL leaders Celtic.
But Draper is determined to show the doubters this season's promise will not evaporate on the back of one week.
Inverness have come a long way since Terry Butcher assembled his team following a number of departures at the end of last season.
The previous visit of Celtic in August saw Neil Lennon's men win 4-2 but Draper's two late goals ensured the scoreline very much flattered Inverness.
But they subsequently only lost to Motherwell between that game and their current three-game losing run and won at Parkhead in November to prove wrong those who wrote off Inverness after that comprehensive defeat against Celtic.
Draper, who arrived from Macclesfield in the summer, said: "People are entitled to their opinion but we had a new team coming together.
"I think we have shown 20 games later, they are eating their own words. We have shown what we can do as a team that's used to each other.
"People are entitled to their opinions but it's nice to prove them wrong sometimes.
"The Celtic game at home was early doors, we hadn't moulded together as a team. We had a number of new faces and basically had a back four that hadn't played together.
"It took us maybe seven or eight games to get going and get our run started. We don't read too much into that game at home.
"The lads were terrific, I went down to watch them when I was injured, away from home against Celtic. Celtic are aware we could cause an upset on Saturday."
Draper insists nothing has changed in their approach since their losing run, which has seen luck go against Butcher's side.
They lost on penalties against Hearts in the Scottish Communities League Cup semi-final, were beaten by a late goal at St Mirren Park, and lost captain Richie Foran and playmaker Andrew Shinnie to injury in the first half of their William Hill Scottish Cup defeat by Kilmarnock.
And Draper has now set his sights on ensuring they make their season count as they look to hold on to second place in the SPL.
"It's more realistic now," he said. "Early on in the season people were saying: 'When is the bubble going to burst? They haven't got the squad to finish in the top six'.
"I think we have proved we can do that throughout the season.
"It might be a blessing in disguise that we have dropped out of the two cups so we can concentrate on the league and finish as high as possible. "Top six is very realistic for us but we want to finish in the top two or three if we can."
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