The Dutch forward was reflecting on what he believes was a missed opportunity in Wednesday night's 2-0 defeat by AC Milan in the San Siro.
Although keeper Fraser Forster was called into action four or five times, the Scottish champions might have nicked a goal their possession arguably deserved.
Striker Anthony Stokes had a shot blocked in the first half before his second-half free-kick from 25 yards clipped the crossbar before going over.
Georgios Samaras drove wide from distance just after the break while skipper Scott Brown hesitated enough when he was sent through by Kris Commons to allow AC Milan midfielder Nigel De Jong to make a crucial saving tackle.
Celtic still looked as though they would leave Italy with a point until defender Cristian Zapata's drive in the 82nd minute deflected off Parkhead left-back Emilio Izaguirre and ended up behind Forster.
The Englishman was beaten again four minutes later despite making a great save from Mario Balotelli's free-kick, as midfielder Sulley Muntari knocked in the rebound.
With Barcelona next up at Parkhead at the start of October, Boerrigter insists the Hoops must be better in front of goal in their remaining Group H matches.
He told STV: "We played pretty well but the most important thing about a game is to win and if you want to win you need to score.
"We got a lot of chances but didn't score. Yeah it was a missed opportunity.
"Milan has some good players and [we knew] if we didn't score then they might and they did.
"We were in control of the midfield with good possession so compliments to the team for that. But then again up front you don't get many chances and when you do, you need to score."
Despite the defeat Boerrigter believes the Parkhead men performed well enough against the Italian giants to recover and be a force in the group.
He added: "We have got a lot of games left so I think we can win some games to remain in the Champions League and that's what we will have to do."