Victories over Newcastle and Norwich, as well as a 1-1 draw with fellow strugglers QPR, had eased tensions in the camp.
But back-to-back defeats against Manchester City and West Ham have left them three points behind 17th-placed Aston Villa with a game in hand ahead of the crucial clash with Spurs at the DW Stadium.
"We have to try and bridge that gap between ourselves and safety as quickly as possible," Boyce told the Wigan Evening Post.
"A lot of the teams at the bottom are playing each other over the next couple of weeks so that's a good opportunity for us to make up some ground.
"But we need also to maximise our own points tally, which includes winning our game in hand.
"Spurs are flying but, before last week, so were we, and it's vital we get back to that form quickly.
"Both teams need to win, there should be plenty of chances, it should be an entertaining game to watch, and hopefully that will suit us as the home side.
"If we can keep their main threats quiet and take our chances, hopefully the three points are there for us.
"We have been here before, heading into the last month and having to win every week."
Roberto Martinez's side face City in the FA Cup final on 11 May but Boyce's focus is on Premier League survival.
"The last thing we want to be doing is going to the FA Cup final thinking about the more important game we've got coming up the following Tuesday in the league.
"It looks like that might have to be the case anyway given the situation at the moment, but if we have to do that then that's the way it is.
"We've still got Spurs, Swansea and Aston Villa left at home - that's nine points to go at. And we're quietly confident that, if it comes down to us and Villa on the last day, we can beat them."