The Ukrainian defeated the defending champion in four sets on Wednesday evening to secure his place in the third round of the competition.
"When you play Federer at Wimbledon, it's like you're playing two people," BBC Sport quotes Stakhovsky as saying. "Federer and his ego.
"I hoped he wouldn't get too far away from me and I hung in there every game on my serve, trying to play for a tie-break.
"It was magic, I couldn't play any better today. Every important point I played well and I served and volleyed incredibly well."
Stakhovsky's previous best Wimbledon campaign came in 2011 when he reached the second round of the tournament.