The profligate Paisley side wasted a string of chances before eventually going down 3-1 at Kilmarnock in SPL action on Saturday.
Now Lennon is determined that his men will make the most of home advantage to knock Accies out of cup competition for the second successive campaign.
Last term Billy Reid's Irn-Bru First Division side held Saints to a 0-0 draw in at New Douglas Park in a Scottish Cup fifth round tie before losing the replay thanks to Graham Carey's winner.
But the Buddies boss has no doubt his side will need to find a cutting edge to their play if they want to progress tonight.
He said: "We need to provide a response to the defeat on Saturday. When we have suffered a set back in the past we have been very positive.
"Hamilton proved tough and well organised last season when they forced us to a replay and we will be taking them very seriously.
"But the big plus for us is that we have home advantage in the tie unlike last season and it is up to us to make the most of that. What is essential is that we find some cutting edge.
"The big problem for us at Kilmarnock was that we just did not take our chances. We created some excellent opportunities in the first half and had we taken even a proportion of them then the outcome would have been different.
"That said, if we can continue to create that level and quality of chances I am sure we will make the most of them."
tonight's tussle with the Accies will be the second round on the trot that Saints will come up against First Division opposition at home with Ayr United being despatched 5-1 last round.
Lennon admitted he would be delighted with a repeat of that five-star performance.
The Buddies boss said: "What was most pleasing about that performance was the tempo we played at and the number of chances we created.
"But there were also a lot of positives to be taken from the Kilmarnock game and we will keep everything in proportion.
"The great thing for us is that after the frustration of that defeat we have a quick turn around and opportunity to put things right.
"I always believe that if you do well in the cup competitions it can have a positive effect on your league form and it's up to us to make the most of it."