The winger contentously won the penalty in the first half, allowing Scott Sinclair to cancel out Robin van Persie's opener.
"It was a clear penalty, the Arsenal player caught my standing leg," Dyer told Sky Sports News.
"A result like this gives us massive confidence. We showed we can match one of the best sides in the Premier League at their style of play."
The win has taken the Swans up to 10th in the Premier League table.