Lennon guided the Paisley outfit to their first trophy win in 26 years last season with a 3-2 Hampden triumph over Hearts.
But Saints have failed to build on that victory and now face a fight for Scottish Premiership survival.
Just four points separate four teams in the scrap to avoid finishing in 11th place, with St Mirren only a point better off than Ross County and Partick Thistle - and three behind Kilmarnock, who have played a game more.
Lennon said: "Winning the cup was fantastic but, as a manager, I know it's important not to dwell on the past.
"It's been a rollercoaster season for us. The media will want to now bring up the fact it is a year since we won the cup and the supporters will want to celebrate that fact.
"But managers are not judged on what happens in the past - they are judged on the here and now and that's where my focus is.
"We want to pick up as many points as we can in the last five games before the split and get us up that table."
But Saints could not have been handed a harder run-in, with five games against top-six opposition.
They take on Dundee United at Tannadice on Saturday before clashes with Celtic, St Johnstone, Inverness and Motherwell.
Lennon, though, remains confident his side can fight their way out of trouble.
He said: "Our destiny is on our own hands. We are where we are. We will focus on building on the positive result we got against Kilmarnock last week.
"We are facing an in-form Dundee United side but no-one gave us a chance against them on Boxing Day when they had just won six straight games. We got a 4-1 win that day and we'll look to do the same again.
"I believe that if you take Celtic out of this league, you can look at all the other teams as being compared similarly. What these top-six clubs have done is be more consistent than the sides in the bottom half of the table. But on the day anything can happen."