Andre Villas-Boas's side came from behind to secure the three points at Upton Park which pushed them up to third in the Premier League table.
"I've been in that position when you're playing and you're watching the scores come in and you hear there's been a last-minute goal in a game that's important for your side," Parker told reporters.
"You're praying it's gone the way you wanted it to and then you hear it's a goal for the team you didn't want to score. So it is deflating for a player watching, and I'm sure the Arsenal players are like that."
Tottenham and Arsenal face off in the North London derby on Sunday.