Cockerill took over from South African Heyneke Meyer
Leicester Tigers acting head coach Richard Cockerill wants his side to finish in a top four Premiership spot.
The Tigers managed a 28-31 win at London Irish on Sunday.
Cockerill told BBC Radio Leicester: "We just need now to make sure we knock off those teams above us and it keeps closing the gap.
"We're looking to finish top two as we want a home draw or top four gives us a play-off and getting back into Europe as a guarantee is also a prerequisite."
Cockerill added: "So, we need to keep working hard on the training field and try and improve week on week."
The Tigers are currently fifth in the table with 43 points.
They face Gloucester at home in the Premiership on Saturday.
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