After welcoming eight players back from international duties, Tigers took the points with four penalties from captain Toby Flood, though they did have to survive a last-minute Exeter penalty which could have levelled the scores.
“This is a tough place to come,” said Tigers director of rugby Cockerill after the win at Sandy Park.
“We’ve not had our England players for eight weeks, we got them back on Monday and had to get them integrated this week and playing again. Coming here first up is a tough call.
“We could have been better at times, but the attitude was great and the points are key.
“There was one good chance in the first half which could have stretched our lead but it wasn’t to be. We were a little bit rusty and up against a very motivated team, which is a tough combination.
“In the first half we were relatively pleased, we were pretty controlled playing into the breeze, but in the second half we never quite had enough to stretch out. Exeter just don’t go away do they? They’re very committed, very physical and they make you work hard.
“They could have levelled it with that penalty at the end and we probably couldn’t have complained if they had. But we needed the win to keep us up in the top four. We take the points and move on.”
Cockerill praised the players who returned from the England squad at the Six Nations and bounced back after the disappointment of defeat against Wales last weekend.
“The England guys were good,” he said. “It can be hard with being away for a long time, the travelling, the other duties around that and the pressure of the games. But from my own experience, what you want is just to get straight back into it at your club.
“Those guys all wanted to play and we needed them. You cannot leave your Test boys out here because of the respect we have for Exeter and their record here.”
Tigers are on the road again in Round 19 as they go to fourth-placed Northampton Saints on Saturday (3pm). The next home game in the Aviva Premiership is against London Wasps on Sunday, April 14 (3.45pm). Tickets are available now.