The Hoops manager has detected a "flatness" about his players in the two games following their Champions League last-16 exit to Juventus earlier in the month.
Celtic had to come back from 3-1 down at home to Aberdeen in the match immediately before the international break to win 4-3 with a last-gasp goal from Georgios Samaras.
The week before that the Parkhead men surrendered a two-goal lead to lose 3-2 to Ross County in Dingwall and the former Celtic skipper is looking for the leaks to be plugged against the Scottish Communities League Cup winners.
"I think there has been a bit of a flatness since the Juventus game," he said. "However, certainly the last half-hour (against Aberdeen) filled me with a lot of excitement and satisfaction in the end.
"But the goals we have conceded in the previous two games were poor and that is something we need to brush up on."
Lennon is hoping the international break has rejuvenated his players as they close in on the title and look to get past Dundee United in the William Hill Scottish Cup semi-final at Hampden next month.
"You always think it is never a good time to have a two-week break but maybe it was what some of them needed," he said. "We are looking for a real charge over the next month or so."
In tribute to St Mirren's League Cup final win over Hearts at Hampden almost a fortnight ago, Celtic will form a guard of honour for the Saints players before the game. Lennon believes the Buddies' players will still be buoyed after bringing the first bit of silverware back to the town since 1987.
The Irishman said: "They will probably still be on a high. It is a great achievement for them, their first trophy in 26 years, and they are playing us so that usually brings out the best in teams."
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