The Scottish champions were hammered 6-1 by Barcelona at the Nou Camp on Wednesday as they finished rock bottom of Group H.
It was a far cry from last year's European campaign which saw them beat the Catalan giants on their way to the last 16.
Following that painful midweek defeat, midfielder Kris Commons claimed the club need to abandon their buy-cheap-sell-high approach and instead invest heavily on quality targets if they were to compete with the continent's biggest sides.
But Lennon - who admitted his side were financial "lightweights" compared to group-stage opponents Barca, AC Milan and Ajax - believes that is too much of a gamble with the club's meagre resources.
"It's not that it's hard to compete with these sides financially, it's impossible," said the Northern Irishman. "Barcelona's wage bill is £210million. Ours is a fraction of that.
"We are in a difficult position because of where we play our football domestically.
"When you have three qualifiers you have no guarantee that you will get to the Champions League. When you do [qualify], you have a two-week window to attract players and that is a difficult thing to do. Even when we bought Virgil Van Dijk and Amido Balde in June, we only had three weeks before we were playing qualifiers.
"Even if we has spent £7million on a striker, would that have guaranteed us getting into the last 16?
"Shakhtar Donetsk spent £160million and didn't qualify. Juventus didn't, Naopli didn't, neither did Benfica. We overachieved last year [when we got to the last 16] but this time finished fourth in a group where we were seeded fourth. It is what it is."
He added: "But the challenge of it is to try and compete on the pitch. Somewhere in the back of my crappy old mind, I think we can beat these sides. Sometimes you get a bloody nose and sometimes you get a result like last year when we beat Barcelona."
But Lennon - who attended a board meeting on Friday morning - refused to take issue with Commons' outburst, saying: "Look, I did the same in 2005 after we lost to Shakhtar Donetsk. Dermot Desmond spoke to me after and made it pretty clear where we are. Maybe Kris needs to be made aware of that too.
"In the raw emotion of a defeat like that things can get said that maybe he means but probably doesn't understand the full story. Maybe for some of the senior players it's important we sit them down and explain where we really are."
They replaced the trio with Amido Balde, Virgil van Dijk, Steven Mouyokolo, Derk Boerrigter, Nir Biton and Teemu Pukki but Lennon denied the club had spent figures approaching £3million for any of the incomers.
And he snapped at suggestions that the club had not spent well in recent years.
"We have had value for money," said the former club captain. "Van Dijk I think was value for money. Bitton will be. Pukki hopefully will be.
"Adam Matthews, Mikael Lustig, Emilio Izaguirre, Victor Wanyama, Gary Hooper, Joe Ledley, Charlie Mulgrew, Fraser Forster - do you want me to go on? They have all been value for money, so I think we have done reasonably well with the strategy that has been set for us."
Lennon will now look to next month's transfer window as an opportunity to improve his squad and give them six months to settle in before attempting to qualify for Europe's premier club competition for the third year in a row.
He said: "We will always look to invest in the team where we can and we will look to do that in January. That will give us from then to May to get them accustomed to the style and environment of the club.
"But right now I'm more concerned with the players I have rather than the players I don't. I was disappointed with a few of them on Wednesday night."
Still angry with his side's display against Barca, Lennon has promised change for Saturday's Scottish Premiership clash with Hibernian at Celtic Park.
He said: "I picked a team to do a job on Wednesday and I have to take responsibility for that. It hurts me more than anyone else. I'm a proud man and I didn't like what I saw in some facets of the game."
- Sports & Recreation
- Kris Commons
- Shakhtar Donetsk
- Virgil Van Dijk