Raggett nodded in with a minute of normal time to go to send Lincoln through and eliminate the Premier League outfit at Turf Moor.
The victors, top of the National League - the fifth tier of English football - are now just one game away from appearing at Wembley in the last four.
Raggett told BT Sport: "I am lost for words, it just shows this group of players are a special group. Unreal."
Burnley's rise to mid-table in the Premier League has been built around a solid home record but they were second best on the day with Lincoln fully meriting their win.
"They are a quality side, they drew with Chelsea here last week so to keep a clean sheet and win the game is amazing," Raggett added.
"We didn't come here for the occasion, we came here to win the game and we believed we could.
"It's crazy, for a non-league team in the quarter-finals of the FA Cup in modern day football, it's unheard of."
Lincoln's celebrations will be kept to a minimum, however, as Raggett explained.
"We have a big game on Tuesday - North Ferriby away!"