"Montpellier will be looking to knock lumps out of us now in their own back yard. But Ulster have won there so we have got to go looking for a win ourselves," said Cockerill.
"We could do with another five points there. That early purple patch we had was as good as we've been for a long time, but then we became inaccurate."
Tigers old boy Jim Hamilton couldn't put his finger on why Montpellier made such a poor start to such a big game, but promised a big reaction in the return fixture.
"Given the way we started the game we didn't deserve to win it, although the way we came back will give us some confidence. We were extremely disappointed not to get the extra bonus point at the end, but credit to Ryan Lamb for that drop goal," said Hamilton.
"We showed a never say die attitude and we seemed to get stronger at a time when some French teams might have died. I can't remember when we last got a poor start like that.
"Next week is a big week for us. Everyone knows what a big tournament the Heineken Cup is and what a great side Leicester Tigers are."