Chelsea's Cesc Fabregas (C) in action with Liverpool's Ragnar Klavan before he gets a red card
A Gary Cahill goal in the early stages of the game settled the contest while Cesc Fabregas was sent off for a challenge on Liverpool defender Ragnar Klavan.
Milner has told the official Liverpool website: "I think it shows both teams wanted to win and there's that competitive edge there.
Liverpool's James Milner
"So even though the result isn't that important, we wanted to win and [put in] 100 per cent tackles - both teams were the same.
"I don't think the pitch helped with the tackles, it was a bit dry at times and the ball got caught up in your feet so that might have added to it."
Liverpool's Alberto Moreno (R) in action with Chelsea's Willian
Fabregas's challenge wasn't the only fierce challenge with Liverpool's Alberto Moreno was booked early on for a challenge on Willian.
In terms of the contest being full blooded, so long as there aren't any any injuries that can't be quickly shaken off then there is no harm in it ahead of the new season - if anything it could probably help for the challenges of the campaign that lies ahead.
Both teams seem to have found their competitive edge just over two weeks before the Premier League season gets underway, and they will be hoping for a better playing surface than they one they found at the Rose Bowl.
Liverpool manager Juergen Klopp after the match