The Hammers were beaten 2-0 at Bayer Leverkusen in the first-leg of their Europa League quarterfinal.
"We came here and said that if we lose, we lose by one," Antonio said. "We're 2-0 down, but we can't give up. We've got to believe in ourselves and that we can turn things around.
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"We need to get one next week, then you never know, try and take it to extra-time and turn things around. We've done it in the last two seasons and, hopefully, we can do it again."
He added: "I've put out tweets for the last two years saying, 'It's not over yet'.
"Normally, we're 1-0 down, but this time it's two, so I'll have to say it twice!
"We have to believe. In football, it's not over until the final whistle goes. We've got another 90 minutes to go, maybe 120 minutes. We keep going, keep pushing and keep believing."