Saints' Club Captain played the first half of the goalless draw in north-eastern Spain, which was settled by a penalty shootout that saw the home side run out 4-1 winners to take home the Trofeo Memorial Quinocho.
And Davis says he was happy with the workout provided by the La Liga outfit with two weeks left until the new season gets underway at West Bromwich Albion on 17th August.
"They were good opposition – they tried to keep possession of the ball a lot, which is going to be the style of play we're going to be up against next season," Kelvin told Saints Player
"It was a decent workout on a decent pitch in front of decent fans with a cup to play for at the end of it.
"We could have been two or three up at half time and coasted through the game, but it wasn't to be.
"We ended up with a penalty shootout where, in typical English style, we put one over the bar and the 'keeper made a good save.
"The reason for being here was to get more playing time, and a few of the lads did that," he continued.
"I thought some of our play was very, very good. Obviously there are things to work on and the manager wants us to improve on certain things but, from the first day of pre-season to now, you can see a lot of our performances on the training ground coming into games.
"That's obviously pleasing, and hopefully it'll prepare us for the first game of the season. It was a good test and one we should have won, but that's the way it goes."
Davis collects the runners-up trophy at the Estadio Balaídos
From a personal point of view, Davis said he was happy to have kept a shutout before being replaced by Artur Boruc at the break.
He also had praise for defender Maya Yoshida and playmaker Gastón Ramírez, both of whom were making their first pre-season appearances after extended summer breaks.
"We kept a clean sheet throughout the game, and that's obviously important," reflected the goalkeeper.
"We had to be quite lively in certain situations because we gave away a couple of sloppy free-kicks, so we need to sharpen up on a bit of our organisation.
"Our organisation will come – that's something that the manager isn't too worried about in pre-season.
"I thought Maya played very well for his first 45 minutes, and so did Gastón," he added.
"You could see towards the end of the 45 that they were slightly off the pace, but that's down to a lack of a pre-season. It was nice to see them out there and to see everyone come through the game looking stronger."
The First Team now returns to England for two weeks on the training ground ahead of the big kick off at the Hawthorns.
And skipper Kelvin cannot wait to get the new campaign underway: "It's exciting," he affirms. "I was saying only the other day to my family that I'm really looking forward to it.
"The start of the season is a big deal for anyone who's a football fan, so it'll be fantastic to get these last couple of weeks out of the way.
"We'll keep everyone fit and raring to go, and hopefully we can hit the ground running."