Pavlyuchenko, who had just made a mess of a simple finish, reacted angrily to being substituted with 15 minutes to go against City, with Spurs going on to record a 2-1 win. Redknapp appeared to clap sarcastically when his striker headed straight to the dressing room.
"I don't like that," said the Spurs boss. "It's not something I like. You're looking to scrap away."
The manager added: "The fans are here and paying their money to watch and I think when a player runs down the tunnel without sitting down and watching and getting behind the team, I think that is disrespectful to his team-mates."
Pavlyuchenko's future has been in doubt after an inconsistent first season in England.
Redknapp confirmed there would be some players leaving in the summer, with David Bentley among those who could depart.
"David is going to be a player looking at it and thinking 'hang on a minute, I'm not getting in the team even when Aaron Lennon is not fit. Maybe it is time I moved on'," Redknapp said.
"As a person I like him very much, he's a good lad and a good player. I've played differently and changed the way we've played a bit. I've had results so no-one can complain."