Goals after the break from midfielder Joe Ledley and wide-man Georgios Samaras took the Scottish champions into the play-offs with a 4-1 aggregate success, guaranteeing the Scottish champions at least a place in the group stages of the Europa League.
Asked if it was important for him to get through against the Finnish club, the Parkhead boss said: "Yes I do, just for my own sanity. I have been agonising over this tie for a long, long time, probably since we picked up the (league) trophy in May."
Lennon added: "I have been in a wee bubble for the last six or seven weeks so it's big relief for myself and a big release of pressure. It was a really tough tie. The first goal was huge, if it had gone to HJK Helsinki it would have given them a massive lift but overall, on the balance of the game, we were the far superior team.
"It was a really tough tie. Psychologically for me, it is big because I haven't got through the last couple of years but we have built a good team here and they delivered and answered a lot of questions."
Lennon was extra pleased that his side's victory had been deserved and indeed would have been more convincing had Scott Brown and Samaras converted chances early in the game.
"I am thrilled, absolutely thrilled for the players, the backroom team, the supporters and the club," said the Northern Irishman. "It is a step in the right direction. The players did the business and they came good and I think it was convincing.
"We weathered the storm after the break and scored two wonderful goals so I could not be more proud of the players. For us to play as well as that was terrific. We will see what the draw brings, we are not getting carried away but this will give the players a huge shot in the arm."
Midfielder Victor Wanyama was sent off in the second half with the score at 1-0 after picking up the second of two yellow cards while skipper Brown, Kris Commons, Charlie Mulgrew and substitute Beram Kayal also found themselves in Austrian referee Robert Schorgenhofer's book.
Lennon was clearly unhappy with the official but would only say: "I don't want to take the gloss off the night but to say the referee was inconsistent is an understatement. I am not going to go any further than that but it seems we play a different game on the continent than we do in Britain."