Cockerill told BBC East Midlands Today: "We're better than that. We scored five tries and did some fantastic things.
"But we conceded two intercept tries and if you give Saints easy points they are very hard to chase."
A last-gasp intercepted pass had also cost Tigers certain victory
at home to Gloucester on 16 April
but, with 10 minutes remaining, against Irish the reigning champions turned on the style to win 32-23.
The victory secured a home play-off tie against the Heineken Cup finalists and top spot in the regular Premiership season for the third consecutive season.
Cockerill added: "This is where we wanted to be. We were top after 22 rounds and it shows our consistency and reliance is very, very good. We would like to make life a little bit easier by playing a little bit better at times.
"The fight and fightback was outstanding but we need to make sure we don't get ourselves in to that sort of while in the first place.
Home play-off advantage is massive - Croft
"The players know they need to be better they don't need me to tell them that - I might remind them - but they know they are experienced and good enough, and in many cases they know more about it than I do.
Saturday will mark Leicester's seventh consecutive Premiership semi-final appearance and they have only missed three of the last 10 finals.
In contrast the Saints have never reached a final but they are in form with only one defeat in their last 10 Premiership and Heineken Cup matches.
"We are treating Saints with a huge amount of respect; they are one of the best sides in Europe, they are unbeaten in Europe and can potentially do the double.
"It's knockout rugby. If we lose we are out and finishing top counts for nothing so we have to get it right and we have to win.
"They are a quality side, they are very focused and it will be a hell of a battle. You couldn't have asked for a more mouthwatering clash. It's probably the two best sides in the competition, a local derby and a sell-out. It's what the game is all about."
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