Celtic survive St Johnstone fightback
"We got off to a fantastic start: three great goals and we really should've put the game to bed," Lennon said.
"Gary Hooper has missed two one-on-ones, they were gilt-edged chances.
"I thought our attacking and counter-attacking play was very good but defensively we were poor at times."
"We defended the corners very well and the keeper made a couple of good saves," said Lennon.
"It was a good cup tie and I'm delighted we're in the semi-final; there's room for improvement.
"The first goal we gave away was criminal. We're talking about individual mistakes and then we've been done on a corner kick when we should be dealing with it a lot better.
"We knew St Johnstone would throw things at us but we I felt we were always liable to catch them on the counter attack.
"If we'd have been a bit more careful with the ball, we should've put the game away."
Lennon conceded he would be looking to strengthen his defence during the January transfer window.
"We talk about getting players in and it's an area where we want to improve," he said.
"We'll keep working with the players we've got at the minute until that time comes round - then we'll look at the situation."
Lennon also praised goalkeeper Fraser Forster for his injury-time save to deny Jennison Myrie-Williams an equaliser.
"I don't know how he's saved it," said the Celtic boss.
"He couldn't have seen it until late and I think it got a deflection and he's stuck a leg out.
"That'll go a wee bit to eradicating the weekend (Old Firm defeat) but we've got to come here again on Saturday and will have to defend a lot better."