Tigers conceded 14 points in the first seven minutes but managed to score three times through Scott Hamilton (2) and Alesana Tuilagi as they looked to fight back and the visitors were pressing on the Saints line in the closing stages of the game before finishing empty-handed.
After the 27-19 defeat, director of rugby Cockerill said: “We let them get a good start and you can’t do that in this league. We had opportunities but we turned over ball far too much and we gave away too many penalties.
“We’re disappointed in that but, on the credit side, we kept playing and right at the death we’re looking at one more score to take two bonus points out of the game
“Don’t take it away from them, they took the opportunities well, they’re a good side. But we have to be better and more accurate in our work.
“It’s not all doom and gloom, but it is not a great start for us.
“We need to learn our lessons from it and learn quickly.”
Tigers gave league debuts to summer arrivals Thomas Waldrom and George Skivington, while Ed Slater and Manu Tuilagi made their Aviva Premiership Rugby debuts from the replacements bench in the second half.
Toby Flood was replaced just before half-time after picking up a knee injury which will be assessed over the next 48 hours.
Tigers now turn their attention to the opening home game of the season, against Exeter Chiefs on Saturday (5.30pm kick-off).
“Exeter got off to a great start with a win on Saturday and they’ll be feeling good,” said Cockerill. “We’ve got a quick turnaround, we’ll have a look at a few things from today and look to bounce back as quickly as we can.”
