Speaking after the game, he admitted that it had been an uphill struggle at times, but that Gloucester had finished strongly.
"It was quite a battle, especially in the first half with the scrums where we did well to dig in.
"In the second half, towards the back end of the game, it started to open up a bit which worked in our favour a little bit. We just needed a couple more minutes on the clock, as they were there for the taking I'd like to think."
As ever, it's a game of small margins, and it only took a few errors to let Leicester gain the upper hand.
"There were one or two little mistakes, the odd penalty here and there, and that let the back into the game. It's a bit frustrating as we were only five points down, away at Leicester.
"You can't really make mistakes like that, even just a few, at a place like this.
"We're not a million miles away, it's just a few little things to tie in and it could have been a different result."
Gloucester's resilience was on display right until the very final whistle, and Cox stressed that it's part of the team's mental make up this season.
"They threw everything at us in the first half, and all they came away with was three points. They literally threw the kitchen sink at us and we held them off.
"Our mentality is that we play for the full 80 minutes. Any less is just not good enough.
"Everyone buys into that and, towards the end, we just needed one or two more extra minutes. But the boys were still there fighting until the every last minute."