O'Neill pointed out that having such clarity is made more difficult because "we're rotating a bit as well to try and save some legs" during a heavy schedule of games while some new signings and some recovering from injury had not yet "had a proper opportunity".
"For Celtic, generally it can be a trying time, but we have to get through it," O'Neill said.
"I've experienced these in the past and it's a matter of, I think, maybe giving the players confidence again to go and play their very best under difficult circumstances."
O'Neill pointed out that LASK and Benfica - two sides who have humbled Celtic so far this season in Europe - had since proved their respective qualities.
Asked if he agreed with centre-half Liam Scales that it is not a must-win game against Besiktas, the manager said: "We need to get off the mark at some stage.
"I was told that, statistically speaking, any team who's lost their first three games haven't made it through, so it doesn't augur brilliantly for us if that's the case.
"So if we go on for a fourth one then that would be a world record. We're definitely running out of matches, no question about it, but we are capable of still qualifying."
Besiktas, in contrast, sit eighth in the Europa League table after two wins and a draw.
O'Neill reckons the Turkish side will be disappointed to be only sitting fourth in their domestic league but predicts they will be "a real handful", pointing out that striker Oh Hyeon-gyu might have "a point to prove" after an unsuccessful time with Celtic.
The South Korea striker, who scored 12 times in 18 months with Celtic but only started six times, later confirmed just that.
"I'm so excited - it's very special for me to be back here," the 25-year-old said. "It was sometimes hard for me, but Celtic became like my second home.
"Finally I am back here and I have to show them. Maybe I will be emotional if I score."
Besiktas head coach Vincenzo Italiano faced Martin O'Neill's Celtic in the Europa League earlier this year in a 2-2 draw in Bologna.
"I'm very much surprised they have zero points, so we might see a very angry Celtic," he said. "This might complicate our job."