Goals from Mikael Lustig, Georgios Samaras and James Forrest gave the Hoops a comfortable win over the part-time Irish side at Solitude and ensured there is little chance of an upset when the part-time Irish side travel to Parkhead for next Tuesday's return.
The Hoops boss claimed striker Gary Hooper's mooted move to QPR is not yet complete but it is believed some money from the sale of midfielder Victor Wanyama to Southampton, reported to be £12.5million, will be available.
He said: "Talks are still ongoing between Gary and his representatives but no bid has been accepted by us yet.
"Hopefully we've negotiated the tie but we need new bodies in for the next round and we're going to do that. We're actively looking at strengthening the squad as there's money available from the Wanyama transfer. I'd like someone in before the second leg next week if I can so we can bed them in as quickly as possible.
"If we could get one in early next week, I'd be delighted but at the moment we aren't close to anything."
Lennon was pleased with his side's professionalism during a tie which he believed "had banana skin written all over it."
The Northern Irishman said: "That's just what I wanted, it was a perfect evening. There was a real sense of occasion going into the game and I wanted a good performance.
"I'm just delighted with the way everything went, the atmosphere and the performance. It gives us a bit of breathing space now ahead of the second leg.
"I got that because the attitude was right. There was a lot of negativity going into the game on the back of results in Germany but I'm delighted because we showed a lot of quality."
Cliftonville boss Tommy Breslin conceded the tie was over and joked about not making the journey to Glasgow next week.
He said: "I just asked in there, if we don't turn up, will it be just a 2-0 deficit? But they weren't buying it. It was always going to be an important part of preparation for our league season which starts in a month's time.
"We will go over, lick our wounds, have another week's training under our belt and will try to put on a credible performance and not try to concede too many. It is disappointing. I thought the three goals were preventable and at this level you get punished. They are a class act and that's the bottom line.
"Given we were only back a couple of weeks, and we are a part-time team, I thought we performed credibly. I think Celtic would have had a couple of gears to go up if we had scored, so I have no complaints about the result."
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