Boyd gave Killie the lead but that had already been cancelled out by a Gary Harkins goal when the striker saw red for an apparent punch.
St Mirren pressed hard in the closing minutes but they failed to make the most of some sustained pressure and had to settle for their first point of the season.
Lennon said: "We have a lot of creativity in the side, players that can open up defences and for the first 15 minutes and after the sending off I though we produced some great football.
"Gary Harkins produced some great solo runs and balls across the face of the goal and thoroughly deserved his goal. It was a great game of football and Kilmarnock defended admirably when they went down to 10.
"From our point of view we should have gone on to win and it was really a case of two dropped points.
"Steven Thompson has forced two great saves from Craig Samson and we had more chances as Paul McGowan came into the game.
"We want to climb the table and in these circumstances, with an extra man and given the number of chances we created, we need to take maximum points from our home games."
Kilmarnock boss Allan Johnston had mixed emotions and revealed that Boyd had apologised for his behaviour.
"I haven't seen the incident but Boyd has apologised to the boys and he knows it was just a stupid reaction," Johnston said. "It is not like him and I think that he and Jim Goodwin had challenges throughout the game.
"But he is a big player for us and after scoring it was disappointing because we were in control of the match at that stage.
"We were hanging on towards the end but it was a great reaction from the players and they did really well to hold on until the end."