Vine pounced to score after Murray Davidson had bundled the ball towards the line after the Buddies had failed to deal with a Mehdi Abeid corner.
"I thought the first half we handled them very well," said Lennon.
"The pitch certainly wasn't conducive to the way we like to play but we caused one or two problems by going a bit more direct.
"We handled them very well with their threat from set plays, which they are very good at.
"What was very disappointing in the second half was the manner we conceded the goal. That's five games in a row now that we haven't lost a goal from open play.
"And for me it was the worst ball that came in from their set plays, and we didn't handle it. That's the difference between walking away with one point and no points."
Lennon admitted they are still missing injured winger Gary Teale, who is currently out with an abductor strain.
"I certainly know what our downfall is at this minute - that's three games in a row that we haven't scored," added Lennon.
"I know where the problem lies - the quality coming in from wider areas hasn't been the same since Tealey went out."