On Saturday Lennon was involved in an altercation with some supporters behind the dug-out during the 1-0 loss to Inverness Caledonian Thistle, Celtic's third Clydesdale Bank Premier League defeat of the season.
Ambrose sympathised with the fans following another mediocre league performance from the champions but urged them to stick with the team and with Lennon.
"These things come with desperation," said the Nigerian defender. "They [the fans] want us to win but, when we cannot win, you see the other side of them, the ugly side. But this is football. I believe that, with patience, everything works out better than they think. The team is just building up and the injuries coming along do not help. It's affecting the team a bit.
"The fans should stick with us. Before long they will see [improvements] in the team and we will work very hard to make sure they do."
Celtic's performances in the league have fallen far short of the highs achieved in some of their Champions League matches this season but Ambrose denied that the players had any sort of attitude problem. "I wouldn't say that," he responded. "It is difficult. Every team that comes here to face us wants to be like we were against Barcelona and do what we did. I do believe that when we have a fully fit squad we'll do better than we are just now."
It was an enjoyable afternoon for Antonio Reguero. The Inverness goalkeeper was on the books of Real Madrid as a youth player and took great delight in having succeeded where Victor Valdes, the Barcelona No.1 and a childhood rival, failed.
"I don't know why we won and Barcelona didn't," he said. "Sometimes it happens. Barcelona suffered defeat but a simple club like Inverness can win at Celtic Park. It was lovely.
"I played against Barca a few times when I was younger, I even played against Victor Valdes. That was when I was 16 and in the Real Madrid youth team. I remember we played one game that went to penalties. I saved the first one and thought we were going to win – until Valdes saved three."