The Buddies' four-game unbeaten run was shattered by a 4-1 home defeat against Ross County at the weekend, when Derek Adams' men moved to within just one point of Saints in the SPL table.
With the distraction of a glamour game with Celts having a negative impact on his side, Lennon has demanded his men do the Paisley support proud in his first semi-final in charge at the club.
Lennon said: "We know Sunday will prove a real test of character, but that is what we must produce.
"Too many minds were not on the job against County, but there will be no excuses this weekend.
"What we have to do is produce a performance that makes the St Mirren support proud.
"It is a massive game and we will need every one of the boys playing at the top of their game. But I believe if we get that we can give Celtic a run for their money.
"What was particularly disappointing with the County game was we have set ourselves standards of late and fell below them. That can't happen again."
Looking forward to his first semi-final as a manager, Lennon said: "I think it is a huge plus that we have a game of the magnitude of a Scottish Communities League Cup semi-final to come back to after the disappointment of County.
"It will be a proud moment for myself and the players to walk out at the National Stadium on Sunday, but we must produce a performance that fits the occasion.
"We know our record against Celtic has not been good, but this is cup football. Every dog has his day and we are he underdogs."