The Tigers, whose international players only returned on Monday after an absence of eight weeks, ground out a 12-9 victory in front of a sold-out crowd at Sandy Park. The victory moved Leicester up to second place in the table - just a point behind leaders Saracens.
"A 12-all draw would probably have been a fair result to be fair to Exeter - but this is a tough place to come," said Cockerill.
"We worked very hard and we had to integrate players back into the side after international duty. From my own experience, when you have a poor experience with the national side you want to come back to your club and get straight back into it. That is probably what you need rather than having the rest.
"The key thing here is that your bread and butter is at Leicester because whatever happens on Test duty - hopefully it's good things - at some point that will end and you go back to your club."
The sides went in at half-time level with fly-half Gareth Steenson landing three penalties for Exeter and his opposite number, Leicester's captain of the day Toby Flood, matching his efforts. The only points of the second half came through Flood's fourth penalty.
Exeter head coach Rob Baxter said: "We had a kickable shot at goal when it was 9-9 but we turned it down and tapped and then we tapped again instead of clearing our lines with a kick. This gave them a piece of pressure that led to their winning penalty.
"You look at two moments like that and you can pull your hair out thinking about what we are playing at. We do encourage the guys to go for it and make decisions but there were a couple of bad ones.
"When we play the top Premiership sides, when they are coming full on with their internationals back in, you have to make sure that you are in the fight for the full 80 minutes.
"That part of it was fantastic for us but what we have to add to it is, along with all that physical endeavour, those couple of moments of clarity that decide a 12-9 game."