They did hold a 15-point lead over the Scottish Premier League's bottom side Dundee but they passed up a third chance to secure survival and that advantage is now down to eight points.
Dundee are in action on Sunday at home to Aberdeen, but still need to win their last three games and hope that St Mirren fail to pick up a win, either at home to the Dons or away at Kilmarnock on the final day.
"There's no doubt in my mind," Lennon said when asked if his side would survive.
"In so many ways, we have progressed over the season. We've managed to win a national cup. We've gone up two or three rungs on the ladder, but in other ways we've gone back one or two.
"There's been an inconsistency there throughout the season and the league table doesn't lie. There is six very important points remaining and we want all six.
"Hopefully once we get our house in order we can find ourselves one or two places higher up the table."
On his side's performance, he added: "The penalty decision went against us and that's now the third week in row that we have seen dubiety over whether it was the right decision. From where I was, it looked a poor decision.
"The players thought Kenny had taken the ball and I will take their word for it.
"But what is concerning me is the way we are starting games. That's three games in a row that we haven't come out the blocks. That is something we have to address and very quickly for the two remaining games."