Goals in either half from Cenk Tosun and Idrissa Gueye were enough to secure the Toffees a second successive Premier League victory and Allardyce's team have lost just one of their last seven matches - against champions Manchester City.
Despite their good form, criticism from supporters unhappy with the team's style of play persists and Allardyce - who has guided the team from 13th place when he took over in November to their current position of eighth – has issued a response.
"I can't honestly produce any more than I'm doing," said Allardyce in a news conference. "I'm sorry if some fans don't like it, but we're trying as hard as we possibly can – myself, my staff and the players.
"What can I say when you've got 14 points out of seven games when you were faced with the club being in a very difficult position when you arrived?
"I can only say it's just one of those things, and if we keep winning hopefully they (the fans) might change it to love.
"We've got 14 points out of seven games now so we're riding as high as we could possibly ride."
While it is unlikely that Everton will climb any higher than eighth this season, Allardyce praised his players for their commitment late in the season.
Looking ahead to the club's last two games of the season, against Southampton at home and West Ham away, Allardyce said: "I think that the efforts from the players particularly have been fantastic. When you hit that safe 40-point mark it's very easy for a player to think about his holidays and actually switch off.
"We're pushing ourselves as high up the league as we possibly can, we've sat in the top half for nearly the entire time I've been here apart from perhaps a couple of weeks.
"That really is all down to the players' efforts really from day one."
Opposite number David Wagner, whose side are three points clear of the relegation zone, acknowledged the size of the task facing Huddersfield as they bid to avoid the drop.
Town travel to Manchester City and Chelsea before facing Arsenal at home on the last day of the season, and Wagner said: "I'm disappointed. The players gave everything on the pitch today, as the fans did too, but in the end we were beaten by quality.
"We have to deal with it. We had four match points before today and now we have to use one of our remaining three, even though we're playing top quality.
"We are anything but without a chance still. We have 35 points from 35 games and now we will have to take points against one of the top six teams."