The Scottish champions needed an injury-time goal from Charlie Mulgrew to rescue a Scottish Premiership point in the 1-1 draw with Dundee United at Parkhead on Saturday after another afternoon of missed chances.
The Hoops had at least a couple of good opportunities before Stuart Armstrong gave the Tannadice side the lead in the 38th minute with a well-worked and well-taken goal and there was more huffing and puffing from those in green and white thereafter.
Just when it looked like United would get their first win at Celtic Park since Boxing Day 1992, Mulgrew rose in the second of three added minutes to flick a cross from Emilio Izaguirre past Radoslaw Cierzniak to make it 11 league games unbeaten for the league leaders.
However, the Celtic boss knows his side will have to be more positive in front of goal against Ajax if they are to repeat the 2-1 Group H win over the Dutch champions last month which breathed life into their qualifying hopes.
Lennon said: "We had 20 attempts at goal, 10 corners, we've got to do better.
"We keep flashing balls in the box and I always see an opposition defender getting there first, that's something we need to do better. We need to be braver in the final third.
"It's a concern. You keep giving teams encouragement. Dundee United scored a very good goal but didn't create much else.
"The goal gave them something to hang on to. But the amount of chances going begging was frustrating.
"We don't expect to score in injury-time but we always hope.
"There's a great character about the team even when they're not anywhere near their best."
With a view to the Ajax game, the Northern Irishman started with Beram Kayal, Mikael Lustig and Teemu Pukki on the bench, while Georgios Samaras (knee) and Kris Commons (hamstring), almost certain to start in Amsterdam, sat it out.
Lennon said: "Kris was 50/50. Sammy was getting stitches out so wouldn't have made it but they'll both be fit for Wednesday."
Mulgrew insists the crunch game in Holland will take care of itself.
The Scotland international said: "Ajax is a different game altogether, we are away from home and all the pressure will be on them.
"It will be a whole different game but we will need to improve the performance.
"We would like to have won the game against United going into the Ajax game but that is what happens."