With four points from their three group games, Wales finish second in Group A and qualify for the round of 16, where they will face the second-placed team from Group B in Amsterdam on Saturday.
Page credits players for performance
Speaking in the post-match press conference, Page was full of praise for his players in holding Italy to just a single goal under difficult circumstances.
"They've got the job done", he said. " We want to win every game, and I had to make some tough decisions after the game. They thoroughly deserve all the plaudits that they're going to get.
"Credit to the boys, I can't speak highly enough of them, and I couldn't be more proud of them."
Second place good enough to see Dragons into knockout stages
Even with a loss, the Wales coach was more than pleased as the Dragons have qualified for consecutive knockout stages at a major international for the first time in their history.
"It feels like a win because we've got second spot. We knew we were in for a tough game coming into it and we knew we would have to dig deep at times.
"It's tough enough 11 men, but to do it with ten men gives us an even bigger hill to climb. It's a defeat but progressing was our aim and we made it in the top two."
Tactical switch after Ampadu sending off
Page was forced to change his formation after Ethan Ampadu saw a straight red card, but he was satisfied with how his side performed under the circumstances.
"We didn't want the game to open up and be end-to-end. It didn't quite go to plan the press in the first half. We addressed it at halftime and managed to get Ethan Ampadu at the center of the diamond and get him on the ball a little bit more at the start of the second half.
"The sending off changed the course of the game. I haven't seen it again yet. I thought it was harsh to get a booking but to see the red card come out was unbelievable.
"We didn't want to concede two or three goals and we were hoping to use the three up front on the break, but of course when we were down to ten men it was tough and we did well at the back.
"I went with my heart for the last half an hour. Otherwise, we would have been camped on the edge of our box. (Kieffer) Moore did a great job when he came on."