Lennon took over from Brendan Rodgers in February when his fellow Northern Irishman left the Scottish champions for Leicester, and he will remain in charge until at least the end of the season.
Lennon recently guided the club to their eighth successive Scottish Premiership title, but came under fire after Sunday’s 2-0 defeat to fierce rivals Rangers.
A permanent position has yet to be given to Lennon, who spent seven years as a Celtic player, before returning to manage the club for four years in 2010.
"There is no evidence to suggest I can't take the job on,” Lennon said, speaking at the club’s training complex.
"I have been here since 2000 and in that time Celtic have won 14 league titles and I have played a part in 10 of them.
"So I think I know how to win titles here. I think that gets overlooked.”
The former Celtic captain went on to accuse a small group of the club’s fans of taking his success for granted.
"I think there is a new breed of supporters, here or elsewhere,” he said.
“Since 20 years ago the only thing they have seen is success. They don't remember the 1990s as the older generation do.
“I can't take it for granted, they might. That comes from an immaturity from their point of view.
"In present-day football there is always a furore after one game, whether it be social media or phone-ins."
Celtic will be presented with the trophy at Sunday's home game against Hearts, their last league fixture of the season before once again taking on the Edinburgh side in the Scottish Cup final later this month.
"If we win the cup that will be my seventh cup and any time we lost the league that I have been involved in it was on the last day of the season,” said Lennon.
Celtic have the chance to complete an historic domestic treble when they travel to Hampden Park on May 25, which might just be Lennon’s final game in charge of the club.