Eze singled out by Southgate after impressing in first England start
Cole Palmer netted his first goal for England from the penalty spot, while Trent Alexander-Arnold and Harry Kane also scored in the team's penultimate friendly match at St James' Park before heading to Germany for the Euros.
Southgate now needs to cut seven players to meet UEFA's 26-player squad by Friday's deadline, an almost enviable job given what has been touted as one of the most talented groups England has assembled in a while.
"It's a decision that we understand the significance for all of the players and so, we're giving it the respect and consideration it deserves really to make fair, right decisions," the manager said.
"It's always going to be subjective, and we've got to balance what we need in every area of the pitch as well. So that's the added complication."
Crystal Palace forward Eberechi Eze "caught the eye," said Southgate. "The way he started the game and the way he glides past people and the power that he shows," he added.
Alexander-Arnold, Palmer, Conor Gallagher, Adam Wharton and Jack Grealish also impressed the England boss.
"A team that didn't have a lot of caps on the field when we started, but I think it showed the way that we work that people feel comfortable in an England shirt pretty quickly and that was lovely to see," he said.
The Three Lions host Iceland at Wembley on Friday before flying to Germany where they kick off their Group C campaign against Serbia on June 16.
"It's not getting the best individuals in, there's a positional element to that as well," Southgate said. "But we've got really good options and I think we've come through tonight without any physical issues, which was really, really important.
"Some players needed the minutes and they'll need the minutes again on Friday. That's why we brought on Harry Kane (who had not played for Bayern Munich since May 8), he needed some match time today and then to back that up.
"So we're spinning a lot of plates trying to get individuals into things, manage minutes, perform well and everything else, but I think today was a good night for us."
