Tottenham cut Leicester City's lead at the top of the table to five points with their emphatic 4-0 win over Stoke City on Monday.
A comfortable 4-0 win at Stoke City on Monday saw Spurs cut the gap at the top to five points heading into the final four games of the season, with Leicester held to a 2-2 draw by West Ham on Sunday.
And with the title still a real possibility for Mauricio Pochettino's men, Walker insists that the club will now view second place as a disappointment.
"If you had said to me do you want second at the start of the season I'd have said 'Alright thank you and I'll see you next year'," he told the BBC.
"Now I think there's still a lot games to play - a lot of minutes.
"They've still got a couple of difficult fixtures coming up and we need to be ready to pounce when Leicester do mess up."
Leicester could restore their eight-point lead at the top of the table with a win over Swansea at the weekend, with Tottenham taking on West Brom at White Hart Lane the following Monday.
However, Claudio Ranieri's side will have to do so without top scorer Jamie Vardy, who is suspended following his red card last weekend.
And Walker says Spurs are ready to take full advantage, adding that the current crop are among the best to have ever played at the club.
"On paper some of the players who played before. You had Gaz(Gareth Bale], Ledley [King], Luka [Modric].
"But as a togetherness and a team this is by far the best."