The win pushed Arsenal up to 13th in the Premier League and they are now six points off Aston Villa, who are fifth.
And asked how big a boost putting back-to-back wins together is after beating Chelsea and Brighton, Holding replied: “It is a massive confidence boost for us.
“Obviously we went through that really rough patch, but as soon as we got a win it gave us a lift.
“Now we’ve got another win and hopefully now we can go on a bit of a run, pick up points and climb up the table.
“Fingers crossed we can climb the league and get back into European places and push on.”
As with Chelsea, manager Mikel Arteta handed chances to Arsenal’s youngsters against Brighton.
Teenagers Bukayo Saka and Gabriel Martinelli started, while Emile Smith Rowe also kept his place in the side.
Smith Rowe has long been tipped for the top at Arsenal and the 20-year-old is relishing getting his chance to shine.
“I’ve really enjoyed it,” he said.
“It’s a dream for me to play for this club. I’m so happy and grateful that the manager’s shown faith in me and given me the chance.
“I’ve just got to keep training hard, and then when I get the opportunity I’ve got to take it.”