Goneva intercepted the ball on his own line as the Falcons piled the pressure on the hosts at Welford Road, sprinting the length of the field to complete a 17-minute hat-trick and effectively seal the points for his side with 20 minutes to play.
"Niki's third try was a bit fortunate but he backed himself and got the interception. It was a 14-pointer. It was seven points either way, and fortunately it went ours," Cockerill is quoted as saying by PA.
"I'm happy with the five points, there's lots of work to do but we have some injury issues and it was a potential banana skin.
"I thought we coped well with the cheap try just after half time. We kept our composure, got back into it and scored the tries. In the first half we were just finding our feet."
Leicester's next match sees them take on Exeter Chiefs at Sandy Park.