Avenue boss Trevor Storton said the scoreline flattered City: "To say we had five or six of our players missing because of holidays and work, and remember it was our first game and even the first time we have worked out on the pitch since last season, then I don't think we did too badly at all.
"It was a shame the two late goals went in because 4-0 looks like a walkover and our lads were better than that."
But Tigers manager Peter Taylor was happy with the performance: "The pitch was hard and the bounce was very unpredictable so it was a bit difficult at times getting the ball down.
"In the first half, we scored two excellent goals and all credit to Ryan Williams and Ben Burgess as they were top class finishes.
"In the second half, I didn't think we did as well. We tended to complicate things a bit, but I can't complain so far."
Meanwhile, midfielder Ian Ashbee added his praise: "Overall, we're stronger than last season, particularly in terms of scoring goals, and I think the squad is a lot stronger. We've got a lot more genuine competition now.
"Although it is going to be tough next season, we're one of the biggest, if not the biggest clubs, in the division. We should be there - and we will be there. We want to be in the mix-up, not just for the play-offs but for the top three."
The 26-year-old made his first appearance since suffering an injury in March last night, and reported a successful comeback: "There are no problems with the ankle and it's great to be back."