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Pavlyuchenko came off the bench to get the only goal in Tottenham's 1-0 win over Sunderland at White Hart Lane on Sunday as the north London club rose to third in the Premier League.
The 61st minute strike was the Russia forward's first goal in the Premier League this season and he has been given few chances to chances to break his duck before now as Redknapp prefers Emmanuel Adebayor and Rafael van der Vaart as his main attacking options.
With Euro 2012 just months away, Pavlyuchenko has made it clear he would like to play more often.
But Redknapp, who has England striker Jermain Defoe in a similar situation, is adamant that nobody will be leaving White Hart Lane in January as Spurs chase a top four finish and possibly a challenge for the Premier League title.
"Somebody's got to be unhappy. The ones you pick love you, the ones you don't can't stand the sight of you," Redknapp said.
"Pav is a fantastic player, he's got great ability, he's a great finisher - top drawer as a player. But he's been unlucky.
"Rafael van der Vaart, Adebayor and Jermain Defoe have been in great form. He didn't start the season well and has slipped down the pecking order a bit.
"It is difficult, he's an international player, who has got the Euros coming up and of course wants to play. It's hard.
"It's like Defoe. He wants to play. He wants to get back in the England squad. It's hard. Somebody's got to be left out.
"But I would keep all four of them, I would like to keep them all. You need your strikers. It is like central defenders, you have four or five then you lose a few."
Pavlyuchenko didn't help his cause with a rather lacklustre approach to getting ready to come on as a first half replacement for Aaron Lennon.
Tottenham lost England winger Lennon after just 26 minutes to a torn hamstring, which was the cue for Pavlyuchenko's introduction.
But the Russian looked as if he didn't expect to be called up and Redknapp made his feelings clear to his striker.
When you put on a sub you expect them to be ready," Redknapp added. "Pav hadn't warmed up an awful lot.
"He did nothing especially wrong. It was just me doing my nut for a change.
"I could have got Niko Kranjcar on, I could have brought Steven Pienaar on, but I thought the game was going to be tight. If you want someone to score, he is always likely to score."
Spurs were without Wales winger Gareth Bale but Redknapp expects him back from an ankle injury in time for Thursday's match against Chelsea, although Lennon could be out for a several weeks.
Meanwhile, Sunderland manager Martin O'Neill, who suffered his first defeat in his second match since replacing Steve Bruce, admitted he will continue to play Nicklas Bendtner, Lee Cattermole and Titus Bramble despite their off-pitch misdemeanours.
Bendtner and Cattermole were arrested on Thursday after allegedly vandalising cars in Newcastle, while Bramble is on bail after being questioned by police over an alleged sexual assault and possession of a Class A drug.
O'Neill, who revealed he had spoken to all three players about the alleged incidents, said: "We will deal with it when the police finish their investigations.
"That's what you have to do. It is not avoiding the issue."
