Leicester Tigers ran in tries from Toby Flood (2), Alesana Tuilagi and Horacio Agulla to move into second place in the Aviva Premiership table with just two rounds remaining.
“Saints are a very good side, but I thought we were outstanding,” said director of rugby Cockerill after a 35-21 victory.
“We’ve not won at Franklin’s Gardens for six years, we know it is a difficult place to win and they are a very dangerous team, so we have to be happy with where we are.
“The last time we came to Saints we got beaten in the first 20 minutes, they bulldozed us. You have to match the physicality and you have to be accurate. We were a bit sloppy on occasions and they punished us for that. They could have scored first, but we kept at them and we got a very good result.”
Tigers set a Premiership Rugby record with a fifth successive bonus-point victory, but competition is tight at the top of the table going into the last two rounds.
“We’re on a good run. We’ve been playing well, we’ve got a healthy squad with strength in depth, and you need a bit of luck along the way too,” said Cockerill.
“Now we’ve got Quins away and Bath at home, so there are two more tough games to come in the league.
“We just have to keep getting our bits right and hopefully that can put us in a good place.”
Tigers are at league leaders Harlequins on Saturday (3.15pm) and then host Bath in a sell-out fixture at Welford Road on Saturday, May 5 (2pm).