Trailing 2-0 from the first leg, Kris Commons netted the vital opener in first-half injury time before Georgios Samaras added a second three minutes after the break to level the tie.
James Forrest then scored in injury time to send Celtic Park wild and the Hoops into Thursday's lucrative group stage draw.
Lennon told Sky Sports: "This is the greatest night of my footballing life.
"I know it doesn't mean a lot in the footballing world but what we've come through in the last six or seven weeks has been really difficult and to achieve more or less I think the impossible tonight, speaks volumes for the players in that dressing room and my backroom staff - they've been planning this for a long, long time.
"I've just got a huge feeling of relief but a huge feeling of pride, I don't want to go through this again!"
Lennon had the utmost praise for match-winner Forrest and the rest of his players.
"For some reason there's a section of our support that can't take to him but I don't know why. I thought he was wonderful tonight.
"He's had a lot of injury problems. (He's had) a sciatic problem that we've been working very hard on in the background just to try and get him on the pitch because when he's on the pitch he's such a special player.
"But they were all heroes tonight. You know (Efe) Ambrose and (Mikael) Lustig and (Adam) Matthews.
"They were looking dead on their feet really and you were just thinking maybe one more last hurrah, could we nick it, and just that feeling of euphoria at the end, just knowing we're going to the big show again.
"There's been a lot of negativity this week (after the first leg loss) but they certainly got what they deserved tonight."
The Hoops boss admitted he hoped to bring in some new signings, saying: "I need help because I haven't much of that in the way of that.
"It makes the achievement more remarkable."
On who he would like to face in the group stage, Lennon chose Real Madrid and added: "I think that would be pretty special.
"Or maybe a Battle of Britain would be great as well, but I don't care - it's just a magnificent feeling.
"I'm delighted for the players and supporters."
You can watch the Champions League draw live on Sky Sports News from 4pm