Irishman Lennon took over from former manager Tony Mowbray in March with Old Firm rivals Rangers on their way to their second successive SPL title.
And although the Parkhead side finished the season with eight straight SPL wins, they were knocked out of the Scottish Cup by First Division Ross County.
Celtic were dumped out of the Champions League and Europa League qualifiers at the start of this season before going on another eight-game winning run in the SPL - only to lose at home in the top-of-the-table clash with Old Firm rivals Rangers on Sunday.
However, Wilson, 26, does not buy in to the idea that the Hoops do not have the players for the big occasion.
"I don't believe that," the former Dundee United skipper said.
"We have players who have played in the World Cup and Champions League and won league championships.
"We have a wealth of experience here.
"It's not come together the way we have liked in the previous big games but there are plenty big games to come and I'm sure in those games we will show how good we are."
Wilson joined his boyhood heroes in January 2006, when Gordon Strachan was boss, and he suffered like many Celtic fans during Mowbray's ill-fated spell as manager.
The full-back claims the Celtic dressing room is as united as it has ever been.
"The first Celtic squad I joined was already full of winners and full of experience in this league," the former Scotland Under-21 player said.
"A lot of them had played under Martin O'Neill and won a lot of championships.
"This squad is fresh. The players have played in the big occasions but haven't won the league so that is going to be a challenge.
"But there is a massive difference in the dressing room.
"This dressing room is very close, very upbeat and lively, whereas when I came in the big hitters stayed away from the small guys like me.
"But that team was very successful and I'm pretty confident this team can be pretty successful too.
"I have a pretty good feeling about this.
"I don't want to slag anyone off but in the last few (years), the atmosphere wasn't the same.
"It was a bit down in the dressing room and some of the players didn't connect.
"This backroom has brought in players and staff that really do connect.
"We have nights out together, golfing days and pool competitions, just things like that can bring a squad close together.
"Last year we were a bit disjointed and certain people didn't mix with other people and it definitely showed on the pitch.
"This year is a lot different and the boys are friends first and foremost, before team-mates.
"It is almost as if the backroom and players merge into one, we have that good a relationship.
"You see when someone scores a goal every player on the pitch runs up to them. It's the relationship we have.
"It's a great workplace to be involved in just now and I think it rubs off on the way you play.
"It's a good feeling and just hopefully we can kick on and go on another good run."
That improved dressing-room spirit did not prevent Wilson from being disappointed at being left out by Lennon for yesterday's Co-operative Insurance Cup quarter-final win over St Johnstone at McDiarmid Park.
The former Tannadice defender, who had battled back from yet another injury to regain his place in the side, was the only unenforced change from the team which lost to Rangers but he does not believe he has been made a scapegoat.
"Obviously I wanted to play but I wasn't picked," Wilson said.
"I wish I could say yes (the manager was being careful with me) but I guess Saturday's SPL game against St Johnstone will be the judge of that.
"I'm feeling fit just now. I have no problems so I want to play every game I can, especially with missing so many games over the years for Celtic.
"There was no conversation. The manager sticks to the same routine, he gives the team talk and reads the team out pretty quickly and you are expected to get on with it.
"(Coach) Alan Thompson had a few word with me and I appreciated that.
"He told me not to be disappointed, that the Rangers game was over and that he didn't want me to think they singled me out for any special criticism.
"He had just felt that Cha Du-Ri was better suited to the game.
"It's up to me just to get on with it.
"The team won and that's the important thing."