The Scottish Communities League Cup winners got back to league business against Celtic on Sunday following their trophy triumph, fighting back from a goal down to snatch a creditable 1-1 draw with the SPL champions. But the point gained was not enough to keep them in the chase for the top six.
However, with the 10th-placed Buddies set to take on Kilmarnock at Rugby Park, Lennon has not yet conceded his hopes of moving up the table.
Saints ended last term in eighth - their best top-flight finish in 21 years - and the former Cowdenbeath boss is hopeful of pairing this season's cup success with another landmark league performance.
Lennon - whose team beat Hearts 3-2 last month to claim their first trophy for 26 years - told Press Association Sport: "The cup win has certainly given us a wee spring in our step and we are hungry for more success. But the league is our bread and butter and we need to improve our performances.
"The table doesn't lie. On a plus side it tells us that we have more points than we had this time last season. We have scored more goals and are closer to the top six in terms of points.
"But on the negative side, we are sitting 10th in the table. However, we believe we can achieve better than that.
"We are progressing and the good news is that the season isn't over yet. We have now got some positive momentum and a strong desire to finish off the season on a high.
"We want to improve on our position of eighth from last season, which was our best finish for 21 years. If we can do that, it will be a very special season."
- Sports & Recreation