The Blues are still waiting for their first win under Benitez after two drab goalless draws at home and fans are still unhappy at the Spaniard's appointment following Roberto Di Matteo's sacking.
Allardyce said: "It was never hate at first sight because he didn't know me and I only knew what he'd done at Valencia.
"But I suppose what he didn't like was getting beaten. You can't get on with everyone in football but my reasons for that stay private.
"All I do is look to compete at a level against not just Chelsea but also against a man who has a real good record, to see if we can upset them and get points off him again. Every manager is different and you weigh up the tactics they like to play and get yours ready.
"If you get it right you can upset the big boys. Liverpool were at the time and we managed to upset them.
"He has been disrespectful to me but it was a long time ago. It's one of those things - we can't all get on, can we?
"The bottom line is whatever managers say between themselves it is still about the players going out there and doing it."