The Paisley side take on Hearts at Hampden next weekend and go into the showpiece game on the back of a hard-earned point.
"It was an evenly contested game," said Lennon.
"We had a few attempts at goal, so we've worked their goalkeeper, and they worked (St Mirren goalkeeper) Craig Samson, who had a fantastic stop from short distance, which was a key moment in the game.
"I'm absolutely delighted that we can go into a full working week of preparation for the cup final with no more games in between. It's been a demanding few weeks for us, but now we can focus on what the talk has been since the semi-final.
"We're just delighted to come out of this game having picked up a valuable point, like every point we've gained this season we've had to fight and scrap.
"After the final, we then come into nine very important league games and that's our bread and butter, what we're primarily judged upon."
The St Mirren boss added that it was natural for his players to have been looking towards the final.
"I'd like to say it hasn't been a distraction but it has, there's no doubt about that," he said. "The players are honest and will tell you that, but that's football.
"Some will be playing in what they feel is the biggest game of their career, and we have a lot of young boys for whom hopefully it's the start, and they have many big games within them.
"We'll leave no stone unturned. We want to go there on Sunday, bring the cup back, and make it a memorable occasion for our fans.
"We have to take the positives out of this game, and look at the negatives and put them right."