Manager Andre Villas-Boas came under pressure after his side slumped to an embarrassing 6-0 defeat at the Etihad Stadium in their last league game, capping off a month in which Spurs failed to register a Premier League goal.
Sunday's draw, however, saw Walker and Sandro find the target against the champions and, though Wayne Rooney twice equalised, the right-back was encouraged by the Londoners' display.
"We needed to show the fans something and prove to ourselves we're a top team. We've stayed strong this week," Walker told BT Sport.
|66/1||Tottenham are 66/1 with BetVictor to win the Premier League|
Walker is confident that Tottenham, who remain ninth as a result of Sunday's draw, can finish in the top four.
"We've brought a lot of players in and it might take a bit of time. The players we have got are top-class international players so we'll be up there. I guarantee it," he added.
Villas-Boas was invited to send a message to any frustrated Tottenham fans but declined, instead expressing satisfaction with his team's response to the City defeat.
"To respond in this fashion against a team that has just put five past the second team in Germany [Bayer Leverkusen] was good for us," said the Spurs boss.
"We are extremely happy with the performance, not so much with the result. I think we probably deserved to win the game."