"It was neck and neck, what a battle," said Genge.
"We knew it was going to be tough, we knew we weren't going to get an easy win."
The Tigers captain admitted the Leicester squad didn't make it easy on themselves with an at-times 'giddy' approach.
"Last year, we would have lost that game," he said.
"We were our own worst enemies at time ... got a bit giddy.
"We came out on the right side of it, but we have got to be a lot better next week."
Speaking about his time so far in the role of captain, Genge added: "I'm enjoying it and think I'm building a relatively good rapport with the referees.
"They have been great about it."
Looking ahead to Round 3, Genge believes the challenge is even great with Saracens coming to Mattioli Woods Welford Road.
"They got a bye week, they'll be fresh," said Genge.
"They'll be coming for us, so we have got to get ready."