Midfielder Dylan McGeouch hopes to avoid a repeat of Celtic's infamous loss to Inverness in February 2000, should they meet in the Scottish Cup.
Celtic have been drawn to play the Highland side, or Dunfermline, depending on the outcome of their fourth round replay.
"It's always brought up in this Cup because of the bad result we had a few years ago," said McGeouch.
"But we believe we're good enough to do well to get to the next round."
Inverness famously defeated Celtic 3-1 in a rearranged Scottish Cup tie in Glasgow 12 years ago that resulted in manager John Barnes being sacked - then followed it up in 2003 with another Scottish Cup shock under new manager Martin O'Neill.
However, McGeouch is confident that Celtic's current form should be good enough to overcome Terry Butcher's side should they beat Dunfermline and set up a tie in the Highlands.
"I can remember it, I wasn't too happy about it, being a Celtic fan," said McGeouch.
"But it's all in the past now, and if it is Inverness we get, hopefully we can do well and get through.
"It's a tricky game - Inverness is a bit of a distance away, but we're on a great run just now and the players believe they're good enough to win the competition, so we need to bypass this round and get through to the next one."
The 18-year-old was handed a debut by manager Neil Lennon in November as a substitute against Motherwell, then scored his first goal for the club three weeks later in a 5-0 win against St Mirren.
That win contributed to Celtic's league recovery, clawing back a 15 points gap on rivals Rangers to take top slot in the Scottish Premier League at the end of the year, and McGeouch believes the revival could help Lennon's side take the title.
"We were a few points behind, but we've brought it back and with Rangers dropping points we've kept winning games on a good run," said McGeouch.
"Hopefully, we can keep that up and keep doing well. You never know what will happen at the end of the season.
"The manager believed in the players. Every week, he told us we can still win the league if we keep winning games one at a time - and that's how we approach them.
"The next game is always the most important - keep winning games, keep getting through to the next round."