The former Tigers and England hooker is operating as the club's acting head coach until the arrival of Marcelo Loffreda and has guided the team to fifth place in the table after the first phase of the season.
"In and around the top four in the league was the target after six games and we have done that," said Cockerill after Saturday's 28-20 victory over Worcester Warriors at Welford Road.
"It puts us in a strong position for when we come back to the Guinness Premiership after the two cup competitions. Let's be happy with what we have got so far.
"The players have worked very hard. They have been great, they have had a tough six weeks and have come through it very well. It shows our strength in depth.
"I haven't been in this position before, we've had 12 players at the World Cup plus a head coach, plus injuries to guys like Harry Ellis, and that means it has been tough for all of us but the players have done well."
Ben Herring, Ollie Smith and Benjamin Kayser scored tries in the win over Worcester, a fourth victory of the season and an important one following successive defeats by Gloucester and Saracens. Now only Gloucester and Bath have won more games than Tigers, with Saracens and Harlequins also just ahead in the table after picking up two extra bonus points.
"It was a good win for us, no doubt about that," said Cockerill. "We needed a win after the last two weeks and we got that.
"It is a hard period for us for a number of reasons and we are only going to get stronger with players coming back and a world-class, experienced head coach coming in.
"The boys are pleased with the win and it has kept us in the mix with a lot of strength to come back to us."
Tigers now switch their attention to the EDF Energy Cup and Heineken Cup before returning to league action.
Bath are up first at The Rec on Saturday as Tigers open the defence of the EDF Energy Cup won last season, then Cardiff Blues are the visitors to Welford Road before the trip to Leinster on November 10 for the start of the European campaign.
The Cardiff game will be the first opportunity to welcome back Tigers' World Cup contingent at Welford Road. Tickets are on sale now. Contact the Tigers ticket office on 08701 28 34 30 or go to the ticket section of this website.