Gary Hooper gave Celtic an undeserved lead on 21 minutes but Spartak hit back before the interval through a strike by Brazilian forward Ari.
However, a Kris Commons penalty eight minutes from time secured a 2-1 victory for the Hoops and confirmed their place in the last 16 for the first time since the 2007/08 season.
"The players have been magnificent and it's a monumental achievement on their behalf," said Lennon.
"For the club to be at the big table in the New Year is a phenomenal effort, as is to get 10 points. It's been a very good night us.
"I didn't think we played well in the first half. We got a break with the goal. Gary's a goalscorer and he'll always be in my team because he's a big-game player. We just wanted to get him fit for this game.
"We were slack for the goal. I thought Kelvin (Wilson) was unlucky, but in the second half we were a lot better. We had good control of the game and created good chances.
"We threw Lassad (Nouioui) on because we knew the score in Barcelona and had to go for it. I wanted to win the game anyway. Thankfully it came through for us."
Lennon was unable to watch Commons' late penalty but he was delighted with the winger's overall performance.
"I watched the last couple of penalties and we missed them, so I thought I'd give this one a miss!" he joked.
"Chris showed a lot of character. I thought he was great in all aspects of his game and deserved his goal.
He's taken a bit of a sore one but we're hoping he'll be okay for the weekend.
"He's written his name down in the club's folklore."
Lennon added: "This campaign has been a great learning process for myself but these young lads have grown as we've gone on.
"Is this my greatest night as Celtic manager? Yes. This is the premier event, the toughest of the toughest in terms of football.
"No one gave us a prayer going into this group. Gordon (Strachan) qualified twice for the knockout stages, so to follow in his footsteps is fantastic.
" I'd some great years under Martin O'Neill, who taught more or less everything about the game.
"If it wasn't for those two guys, I probably wouldn't be here. I'd like to thank them for this as well."