The Buddies lost last Saturday against Ross County before being knocked out at the first hurdle in their defence of the Scottish League Cup with an extra-time defeat to Queen of the South.
And things went from bad to worse as Partick escaped from Renfrewshire with the three points despite falling behind to Kenny McLean's 50th-minute strike.
Saints have won just once since lifting the League Cup in March - a meaningless end-of-season victory at Kilmarnock last term - and the furious Paisley public gave Lennon both barrels following the Jags' 2-1 win, secured through strikes by Kallum Higginbotham and Ross Forbes.
But Lennon insists he can turn it around, saying: "We know things need to improve. But there has been many a good manager that has been through the roller-coaster ride I'm currently on and come through at the other end.
"But we need a bit of patience. Football is an emotional game but there have been clubs that have shown patience in similar situations. Look at St Johnstone last season. They were in the same exact position we are in now - one point from four games.
"But they showed patience and Stevie Lomas took them to their highest ever SPL finish and qualifying for Europe.
"Am I worried? I'm concerned. I'm concerned (given) the standards we have set at this club that we go and produce what we did today. We were a shadow of our former selves.
"I spoke to the chairman there and the board have been absolutely fantastic with me. Top drawer. If my journey at this club was to end tomorrow, I would have no regrets. It has been a pleasure to come here and work.
"But it's something I don't want to give up easy. I love a challenge. The part of the journey I'm going through is not nice but it is one I will relish and I will put it in my tool bag and carry it along with me on my hopefully long managerial career."
Lennon handed new signing Stephane Bahoken a start just 24 hours after his arrival in Scotland on a one-year loan switch from Nice.
But after almost grabbing an early goal, the 21-year-old striker's performance grew ever more erratic and he was replaced at half-time.
"I brought him in and hoped he would have an impact because people would not know a lot about him," said Lennon. "But it was difficult for him because he just met the players prior to the game.
"He had to get used to his new team-mates, Scottish football and the pace of the game. At times he showed some very good things. He has got terrific pace and I thought he scored when he made a ball his that he had no right to get to.
"But he was a bit eager at times and was shooting from all ranges at times. But he will get time in the next two weeks to get up to match-fitness."
McLean volleyed home from David van Zanten's low cross five minutes after the break but Saints failed to build on their lead.
That allowed Higginbotham to curl a beautiful finish past on-loan Swansea keeper David Cornell before Forbes fired home the winner with six minutes left.
Thistle boss Alan Archibald was delighted by his newly-promoted side's second top-flight win of the season.
Archibald said: "I was delighted because when we went a goal down last week against Motherwell, we didn't react positively.
"But today it was totally different. We got a great reaction and continued passing the ball. I was delighted to get the two goals on the back of that.
"I'm a wee bit surprised that we have found our feet so quickly but I'm just pleased we have started so well. It gives us confidence.
"Our fans turned out in their numbers again today, so you can see we bring a lot to the Scottish Premiership.But one thing we want to do is to get away from the cuddly-toy image that we are tagged with.
"We believe we are good enough to play here and hopefully we are showing that."