Clyde go down to heavy defeat at Raith Rovers
The ease with which the Kirkcaldy side carved open the Bully Wee defence will be a concern for Lennon, although two late consolation goals put a little bit more respect into the scoreline.
"It's a very sore one to take and I take full responsibility for the way we set up," Lennon said.
"I know in my head what my best formation is and that's what I'll be sticking to.
"I want to apologise to supporters and that's why I went over to them.
"We know this is a step up for us and we played a very good Raith Rovers side today.
"We've got to make sure we always keep ourselves in the game because we're not going to have it our own way in this league.
"These first round of games are going to be a learning curve for everyone, but we've got to learn quickly."
Clyde were eager and competitive in the early exchanges, but once Rovers got their noses in front, the away side were unable to live with their passing and movement.
The opener arrived on 13 minutes with quick feet from Regan Hendry in the box drawing a foul from Kieran Duffie as he was barged off the ball.
Hendry stepped up and confidently sent goalkeeper David Mitchell the wrong way to set Rovers on their way.
Clyde, to their credit, tried to fight back and a sharp turn from Goodwillie earned him a yard of space in the box and David McGurn was forced into action, saving the striker's low drive with his legs.
Rovers second arrived on 24 minutes with the Clyde defence parting, allowing Hendry to pick out Kieron Bowie, who had picked up a great position at the edge of the box, and the 16-year-old picked his spot past Mitchell.
Rovers ended the half firmly in control, and they put the game to bed just four minutes into the second period, with Grant Anderson outpacing the defence to latch onto a glorious through ball from Brad Spencer, before rolling a composed finish beyond Mitchell.
The home side were now enjoying total domination and it was no surprise when they added a fourth on 63 minutes as sub Joao Victoria raced through before finding the bottom corner.
You could sense Raith taking their foot off the pedal at this stage, and a slip from Benedictus with 15 minutes left allowed Goodwillie a clear path to goal, but McGurn produced an excellent save, diving full stretch to push his effort behind.
But just two minutes later, a slack clearance in the Raith defence allowed Ally Love to cross for Goodwillie to send the ball crashing into the net via the underside of the bar.
Disappointingly for Clyde, they allowed Rovers to restore their four-goal advantage immediately with sub Jack Smith getting on the end of a rebound to steer home his first senior goal, with the defence slow to react.
The away side refused to throw in the towel though, and a short free-kick routine saw Love fire the ball into the net from the edge of the box.