The Buddies are set to play Hearts in the Hampden final on March 17 but Lennon is concentrating for the moment solely on a top-six finish in the SPL.
A 1-0 home defeat to Hibernian last week kept Saints second bottom of the table, 15 points ahead of Dundee, who parted company with manager Barry Smith on Wednesday.
The Paisley boss is looking for improvement when he takes his side to St Johnstone on Saturday.
"We have good quality and I certainly believe we failed to show those qualities last week," said Lennon.
"If any of our players have a notion that they can dwindle by until the final - which I don't think is the case - then we certainly won't be at our best on cup final day. We are at our best when we are at it week-in, week-out.
"We have cup final places to play for but the standard of football last week was certainly not our best and not acceptable for important games coming up.
"The players know that and will look to rectify it on Saturday.
"We have a very important game on March 17 but where our bread and butter is and where primarily you are judged upon, is our league position.
"Generally the level of performances since November have been excellent. We have bad days but to get nine or 10 players under-performing is very unusual.
"But after a poor performance, we have always seemed to come back with a positive performance or a result and that is certainly our aim.
"We have a chance of breaking into the top six in the next seven games and we are looking, like many teams, to put a good run together.
"St Johnstone struggled early in the season but managed to go on a fantastic run of five straight wins and have stayed in the top half of the table since.
"If we managed to put that run like that together that would guarantee a top-six finish."
Lennon believes Dundee have gambled in changing their manager in a bid to pull themselves out of the relegation zone but the former Cowdenbeath boss is looking up the table, rather than behind him.
He said: "From their board's point of view, maybe it is the last roll of the dice.
"Maybe they will get someone to come in to give them a little bit of a lift.
"But we can't concentrate on or have any influence over what happens at any other football club.
"We can only make sure that we can control our own future and our own destiny and we sit at this moment in time two or three points better off than we were last season so it shows how competitive the league campaign is."