The veteran 34-year-old was brought in by boss Lennon to bolster attacking options and challenge for the league title, but the Swede has been left frustrated after his lack of involvement.
Ljungberg suffered a minor injury while at Celtic, but even when fit he was told he was only going to be involved in "big games".
He told Swedish publication Aftonbladet: "It's better that it happened when I was 34 rather than 20.
"You want to be professional and you've got to keep on training without complaining.
"I asked why I didn't get to play. I expected him to say something about me not being good enough and that I hadn't shown anything at training or something like that.
"But instead he thought that I was fantastic. That I was outstanding at training and that he wanted to keep me on for many years. I was completely blown away. I had expected a totally different answer.
"He thought that I should be happy (playing the big games) at my age, but I thought the opposite. I wanted to play every game, otherwise I wouldn't have gone there.Ljungberg denied any personal rift with manager Lennon: "Even my team-mates, players I was competing for a spot with, came up to me and asked me if I had been in a fight with Neil, and maybe that was the reason I wasn't playing.
"I got to know the nicest nationality of people that I ever met. The Scots are fantastic, but I never got the chance to show what I can do, and that's frustrating."