His side went down 2-0 against Hibernian at Easter Road as they extended their miserable run of games without victory to six.
Lennon led the team to the Scottish League Cup last term but they have recorded just three Scottish Premiership victories in the whole of 2013 to date.
And there was little sign of an improvement in Leith as they put in an abject display littered with basic errors and shambolic defending as James Collins and Paul Heffernan netted the goals for the hosts.
But Lennon challenged chairman Stewart Gilmour to explain just who could come in and do a better job then he is currently mustering.
He said: "If I did not believe that I was the man for this job, I wouldn't be sitting here. If that decision is taken away from me and I'm no longer required at this football club, then my question would be: What is it that they want the new man to come in and achieve?
"Do they want them to come and make sure the team survives? I've already done that every season I've been here.
"Do they want successful cup runs? I've been in four quarter-finals and won a national cup. Or is it to simply finish higher up the league. I've already given them their highest SPL finish ever.
"There is no guarantee a new manager would even match that, never mind improve on it. I certainly believe that given time and my own ability, I will improve on that."
And he denied he had lost the support of the Saints' dressing room.
"I believe in the character of my group," he said. "Danny Lennon has hand-picked every player in that dressing room. It was myself who handed out the contracts which allow them to go and pay their bills. so there is no doubt in my mind that the players are still with me."
Lennon dropped goalkeeper David Cornell as he instead went with 19-year-old former Blackburn stopper Chris Dillo.
But the teenager's first act was to collect the ball from his own net after skipper Jim Goodwin failed to beat Michael Nelson to Kevin Thomson's lofted free-kick, which the Englishman nodded down for Collins to head home on eight minutes.
Heffernan ensured the strike duo would both score for the second game running as he met Alan Maybury's cross at the near post to score just on the hour mark.
Saints finished with 10 men when Danny Grainger collected his second caution in the matter of minutes by blasting a quick free-kick at Maybury from point-blank range, with referee Steven McLean deeming it unsporting behaviour.
Hibs have now put behind them their early season blip which included the humiliating 9-0 aggregate thumping by Malmo in the Europa League qualifiers and an Edinburgh derby defeat after notching up their fifth game in succession without loss.
Boss Pat Fenlon said: "I'm delighted. I thought it was a real team performance. We were very solid and created some good chances with some good football.
"All footballers are the same. If you win games, you gain some confidence and momentum and it just breeds from there. You can see it in training every day. All we have done is transferred that from the training pitch to here.
"You can't buy confidence. It's about working through the hard days, which we certainly had at the start of the season. It's about believing what you are doing is right and being bold and brave to say we will get it right."