A brace from Ganso saw Sevilla collect all three points at the Estadio Ramon, leaving Granada stuck inside the relegation zone with just five games of the 2016-17 campaign left to play.
Adams has now lost both of his matches since taking charge of the Spanish outfit, but the former Arsenal captain has claimed that he was "very proud" of how his team performed.
"I think Sevilla are a very good team. They've been good for the last 10 years now and it was a very difficult game for us, but I'm very proud of my boys, they stuck with it and I thought we grew in confidence as the game went on," Adams told reporters.
"We have lots of injuries and lots of suspensions. At times with those things, your team can completely fold and you end up losing by lots of goals, but I was very proud of them that they didn't, they kept fighting right to the end.
"We've got a very big game on Tuesday against Malaga now and we're going to fight in that one. The last three games, we've been beaten 3-0 and 2-0, but I don't think that was a fair reflection on both games.
"I think we deserved something out of both games. So, that's behind us now and we have Malaga next, we're going to try and win that one."
Adams was surprisingly named as head coach of the La Liga strugglers last week, although the former England centre-back will only serve as manager of the Spanish side until the end of the season.
The 50-year-old will then revert to his role of helping restructure Granada, with identifying and signing new players a key part of Adams's role moving forward.