Speaking after the draw with Dundee United on Saturday, Lennon said he believed his players have to cope with the pressure which is sure to increase as the season continues.
"That's the expectation level that comes with being at a big club and the players have to live with that and have to get past that," said Lennon.
"It's been like that since I've been here and I'm sure it was like it before that. It's something we have to deal with.
"I don't think it helps at times but I can understand why the fans get a bit anxious as we all do when you are one-nil up with minutes to go. I didn't think we were in massive danger and were hanging on. Dundee United forced a few set-pieces but I always thought we were capable of scoring. I don't know how many good chances we had but it was enough to win the game." Lennon has chopped and changed his central defence all season and, at times, Thomas Rogne and Daniel Majstorovic looked just as uncertain as previous combinations. But Rogne has no problem with the Celtic fans expressing their frustration.
"The crowd is allowed to get nervous, that is part of being a football supporter, you get nervous and you get happy," the Norwegian youngster said. "Of course we hear what they say but I don't think that affected us. We should just have seen the game out. It's very disappointing when it is a game we should have won.
"We could have been two, three or four-up in the first half. But as long as it is only one-nil, there is always the opportunity for the other team to come back. You know all they need is one goal, so you need to be prepared for this and we obviously weren't."