Leicester's fifth successive bonus point win - a Premiership record - meant they leapfrogged champions Saracens and moved into second place with just two games left, away to leaders Harlequins next week followed by Bath at home.
It is a massive boost to Leicester's hopes of a home play-off semi-final as they chase an eighth successive Premiership final appearance.
Cockerill said: "Psychologically, that sends out a massive message to the rest of the sides we are going to play. It's hard to come here and it was a massive game for both teams.
"It was a great win. We had not won here since 2006 and they are a good side. I thought we were outstanding.
"We controlled the set-piece well and created a lot of chances. That is a big result for us.
"I am delighted with the bonus point but any win here would have been a good result.
"A home tie would be key for us because at Welford Road we would back ourselves to beat anyone.
"We have said for the last few weeks we would like a home semi-final. You have to be realistic because the other sides around us are good."
Leicester scored four tries through England fly-half Toby Flood (2) and Horacio Agulla, who also carved out one for fellow winger Alesana Tuilagi with a magical piece of skill.
Flood finished with 25 points altogether to give England boss Stuart Lancaster a hefty nudge in the ribs for the summer tour to South Africa after falling to third in the fly-half pecking order behind Saracens pair Owen Farrell and Charlie Hodgson.
Cockerill said: "He has been playing well. He is just different to the other guys.
"He likes to play with ball in hand and attack the line. Does he kick as well as the other guys? Probably not but his ball playing and ability to get the team playing is fantastic."
After a poor start to the season due to the World Cup, Leicester have now won nine of their last 10 league games, their last defeat coming against Exeter in February.
The Tigers have also beaten Northampton five times in a row and this defeat means Saints drop out of the top four, replaced by Exeter - who pulled off a last-ditch win against Worcester.
It means Northampton's trip to Exeter next Sunday could determine whether they make the play-offs.
The home side scored two tries, through England pair Lee Dickson and Chris Ashton, but left several chances on the field and paid for a leaky defence.
Director of rugby Jim Mallinder said: "It was hugely disappointing. We made a good start but conceded two tries and we were playing catch up from there. Leicester deserved to win.
"We were second best and we need to sort it out. I was happy with the effort but our accuracy was down. We had two or three chances where we could have scored.
"The difference was they were clinical, really clinical. They got into our third, put us under massive pressure and scored.
"The players are down, they are upset. We have lost at home to Leicester, you don't want to do that, but we will come back. We are still in there, still fighting, we are not going to give up."
Mallinder said he did not see centre James Downey's trip on Leicester flanker Julian Salvi but as it was not a red card offence he is unlikely to be cited.
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