The Buddies boss was less than impressed by his side's second home defeat of the campaign at the hands of Inverness last time out.
But Saints still have a chance of claiming a best-ever seventh place if they can triumph at Pittodrie and Dunfermline defeat Kilmarnock at East End Park on Saturday.
Lennon said: "We are going to need a favour from Dunfermline and hope they get the better of Kilmarnock, but our focus remains firmly on going to Aberdeen and getting the win.
" In every respect we have progressed this season, be it clean sheets, points on the board or league position.
"But I said when we couldn't make a top-six place our own that the next target had to be best of the rest and despite the Inverness defeat we go into the last game of the campaign with our hopes of achieving that still alive."
Lennon has also warned his side to come out the traps faster than they did on their last trip to the north east.
Saints were two down inside the first 17 minutes before goals from Kenny McLean and Graham Carey secured a hard-fought point.
The Buddies boss declared: "The one thing you can't do at Pittodrie is to start off the pace. We did that last time and shipped two quick goals early doors.
"Although we showed tremendous spirit that day to battle back and get a point, I will be looking for us to start at a far better tempo this time around.
"I also thought that we were flat early on against Inverness and it is important we don't make that mistake again on Saturday."