Walker was a doubt for today's Premier League victory over Southampton due to an ankle problem but proved his fitness and was picked in the north Londoners' starting line up.
The full-back appeared set to come through the game unscathed but was withdrawn in favour of Kieran Trippier in the closing stages.
Walker's hand was inspected by members of the club's medical staff following his substitution, with the England international appearing to be in a degree of pain, but Pochettino says the change was not an enforced one.
"My decision was not for that [an injury]," said Pochettino.
"We saw when he was out he had a problem with his thumb. But I don't believe it's a big thing."
The defender has subsequently confirmed on his official Twitter account that the injury will not hinder him from joining up with the England squad during the international break.
Walker has started all but one of Tottenham's top-flight fixtures this season and is a key cog in Pochettino's defensive unit.
Spurs have conceded just 21 goals this term - a total only Chelsea can match - and occupy second place in the table after seeing off Claude Puel's side without star striker Harry Kane.
Chelsea remain 10 points clear at the top of the table but defender Jan Vertonghen is convinced he will not give up on his title dream until he sees the Blues lift the trophy.
Meanwhile, Victor Wanyama was also a doubt for this afternoon's clash with his former club but played the full 90 minutes.