The Buddies came agonisingly close to claiming their second Hoops scalp this term on Saturday but came up just short, going down 2-1, as they were knocked out of the William Hill Scottish Cup.
Despite Esmael Goncalves pulling them level at St Mirren Park, Anthony Stokes' header proved decisive for the visitors as they set up a semi-final clash against Dundee United at Hampden.
Next on the agenda for Lennon's side is a SPL clash against bottom club Dundee tomorrow night as they look to haul themselves up the table before they face Hearts in the final of the Scottish Communities League Cup.
Victory over the Jambos last Wednesday had the Buddies rise to tenth in the league table and Lennon is keen to keep moving in the right direction.
He said: "I thought the commitment and belief we had on Saturday was different class and the key qualities we must take into every single game from now until the end of the season.
"We ran the champions very close in yet another major cup tournament in the latter stages.
"We've got to take great belief in that. It's okay doing it one time at Hampden but I thought the performance was right up there.
"We've got to take those standards into every single league game as we know how important that is for us.
"We managed to jump a place in midweek and we want to continue climbing the table.
"It was a beautiful day, a great day for football and great credit to the ground staff and Tommy Docherty for having the pitch in very good condition.
"The fans created a wonderful atmosphere. I'm delighted to see the ticket sales for the final are going very well.
"We're looking forward to that occasion but we have very important league games in which to pick up points first and foremost."