With the Hammers having moved into third spot following the draw with Wimbledon, Anton says:
"There is no reason why we can't do it; they are under pressure and obviously we are as well but we showed on Tuesday we can do it.
"They will be looking at us now, definitely; this is West Ham United, it is not some little club - we are a big club and hopefully we can do it."
Anton accepts that he is playing less regularly at the moment than brother Rio did at his age, and he says:
"I am still going through a learning curve but it is a team game and I am here for the lads as well as myself - which you have got to be, or you don't get anywhere.
"I am enjoying every minute with the gaffer, Granty, Roger, Strudders and Russ - the atmosphere is good and as long as we stay like that and stay together we can only get better.
"We belong in the Premiership and hopefully we will be there next year."
Anton did get a run at left back when he came on for Jon Harley in the second half against Wimbledon, and he adds:
"It is always nice to get on the pitch - and to get a good win at home after Saturday; we showed the fans we can do it against a lower side in the league.
"We came back with that performance and showed we had character after deserved criticism against Walsall."
He was delighted with Matthew Etherington's three goals and says:
"I am very happy for Mattie and it was frustrating for us that he didn't play against Walsall because of a silly sending off that wasn't even his fault.
"But he has come back and shown what an important player he is - he did well.
"I came on and enjoyed every minute of it, and he helped me out tremendously; it is good to play anywhere on the park - and when I do I give my all."