The Paisley side have managed just one draw from their three opening Scottish Premiership games so far.
And their defence of the Scottish League Cup fell at the first hurdle as the holders were knocked out by second-tier opposition Queen of the South on Tuesday night, just six months after they beat Hearts to claim their first major trophy since 1987.
Lennon's woes have only been exacerbated by the fact they have won just once in the period since their Hampden victory back in March.
But the former Cowdenbeath boss - who faces the biggest test of his three-year reign when newly promoted Partick Thistle visit St Mirren Park on Saturday - insists he is capable of turning around Saints' stalled season.
He said: "It's been a slow start from us and we need to improve. But I'm not naive. I'm like every other manger out there. It's a results-driven business.
"My remit when I first came to this club was to make sure we stayed in the division and I've done that. In addition, I have also given the club national silverware for the first time in 26 years and their highest-ever SPL finish.
"So to me, that demonstrates that I can achieve with this club. I believe in the players we have and myself and my own character. And I believe that with our wonderful supporters, we can turn this slow start around."
Lennon has acted swiftly to strengthen his squad following this week's disappointments.
Blackpool winger Jake Caprice made his debut as a late substitute against Queen of the South following his arrival on a year-long loan, while 21-year-old French player Stephane Bahoken will touch down in Scotland on a similar arrangement from parent club Nice.
Midfielder Jon Robertson, however, will play no further part for Saints after he was allowed to return to former club Cowdenbeath.
Partick Thistle's English midfielder James Craigen is still thanking his lucky stars he chose Edinburgh University to further his education after his move north of the border began his journey into the Scottish Premiership.
The 22-year-old started his career at home town club Preston before moving to Edinburgh to undertake a sports business management degree.
He caught the eye playing for the university football team, while also featuring for the Scottish University side and the Great Britain university team.
Craigen knocked back Conference side Tamworth to join Firhill outfit Partick last season and he is enjoying the start to life in the top-flight following Thistle's promotion from the First Division.
"When I left Preston at 18 I decided to go to university in Edinburgh, was there until 21 and signed for Partick last year," he said.
"It was one of the best decisions I ever made. I could have gone to other universities in England but Edinburgh turned out to be a good choice.
"I always thought I had the ability to enter the game at some point. University standard football is not as bad as you think, there are some good players in higher education.
"I didn't give up, I thought it might take me two or three years to get back into it."
Sean Welsh is rated as a doubtful participant in the clash in Paisley on Saturday. The Jags midfielder is still struggling with a dead leg.
Defender Aaron Taylor-Sinclair is also unlikely to be involved due to a calf complaint.