Saints were behind, and then ahead, in a topsy-turvy tie in north London, where a penalty kick from Heung-min Son settled the outcome late in the second period.
"Kicking ourselves a little bit," Redmond told the club's website. "Those minor instances and little lapses in concentration in games that cost you against teams who have amazing quality.
"Coming off the back of playing at Anfield, we've showed a good performance. I think we were the better of the two sides today, but there's lessons to learn.
"We're not afraid to be behind, because we stick to the game plan and we need to progress with that when we go in front as well.
"There's a lot to look back on. In any competition, we want to show how hard we've been working in the last few months to turn our season around.
"An FA Cup run would have been nice, but we've got time now to rest and recuperate and recharge the batteries ahead of the final part of the season.
"We want more. We want to show the opposition, the world and ourselves what we can do. It's all about pushing ourselves and learning lessons every single game."
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