The Bully Wee conceded three times in that opening spell and although David Goodwillie briefly brought them level and then cut the deficit with a second goal – his 100th for the club – Lennon’s side couldn’t repair the damage.
"We lost the game in the first 20 minutes with some poor goals from our point of view.
"Even the first one, we see two wonderful saves from Neil Parry and then for it to come in for a third phase and go in from that distance, we've got to help him out there.
"We got ourselves back into the game - David creating something as he normally does and then slots the penalty away very well - and then the game settles down.
"To be fair to Peterhead they came out of the traps well; they were energetic and we were over-committing and poor to match runs.
"But not coming out and defending and blocking on the line, defending too deep and not getting enough pressure on the ball, these are basic things in football that you take for granted and should be done.
"The second half was a very good performance and had everything in it we needed, apart from a goal.
"For long periods we were very good but the first 25 minutes have killed us and we've got to learn form that.
"We've got to work hard and make sure the level of performance we gave for long periods in the latter stages we give that from the beginning.”