Blues could become the first club to win a major trophy and be relegated from the top flight since Norwich won the League Cup in 1985.
The 2-0 home reversal by Fulham on Sunday leaves Alex McLeish's side only out of the bottom three on goal difference.
Phillips said: "It just wasn't our day and, with the results elsewhere, the pressure is on. Now we've got to show what we are made of. We've done it many a time. We believe we can go to Spurs now and get a result and we've got to go there and do something."
He added: "Our goals difference is better than the others so we were getting that message onto the pitch towards the end saying 'let's try and not concede anymore'.
"It is disappointing but we are still in with a shout and will go to White Hart Lane and give it our best shot.
"Spurs haven't got an awful lot to play for so we'll go there and we've just got to up our game and we've got to be more solid. We will work hard this week with that in mind."
Phillips insists Blues have to concentrate fully on obtaining a result at White Hart Lane rather than worrying about events involving Wigan and Blackpool at Stoke and Manchester United respectively.
He said: "All we can do is effect our own situation. We aren't going to worry about the others. It is a huge game, we know what is stake, and we've got to start preparing straight away, simple as that. We've got a massive job to do but we can do it. It's in there. We've got to lift ourselves and go again."
Phillips believes Blues' lengthy injury list has taken its toll and they ended the Fulham game with 10 men after Lee Bowyer, Stuart Parnaby, Martin Jiranek and Alexander Hleb all came off injured.
He said: "That has been the story of our season. You've seen many of our games and we've had depleted squads. Players have had to play who haven't played for a while."
Source: PA
Source: PA