Steve Bruce's side, who will be without the services of Fernando Forestieri (hamstring) and Lucas Joao (knee) when they go to seventh-placed Derby County on Saturday, are currently on an eight-match unbeaten run.
Seven points from three successive home matches has nudged the Owls up to 13th, just six points shy of the play-off positions.
Palmer said: "The deficit has been halved in the last few weeks and we have given ourselves a fighting chance.
"It’s a bit of a cliche, but we just need to take it game to game. There’s still a lot of games, and we just need to keep it ticking over, and hopefully slowly creep up to what is a strong finish to the season."
After the trip to Pride Park, Wednesday go to struggling Bolton Wanderers before entertaining Blackburn Rovers a week on Saturday.
"To carry on the momentum (over next three games) which we have built up is crucial, if we are to finish strongly," said Palmer, who is expected to be named in Scotland's provisional squad for their European Championship qualifiers later this month. "With three games in a week you can turn a season around. Hopefully we can come out at the end of the week with a nice points tally."
Bruce, who has won five of his seven away matches against Derby in all competitions (L2), has picked up 13 points from seven Championship games as Owls manager - as many as previous boss Jos Luhukay recorded in his last 14 outings.
Full-back Palmer said: "The message to everyone is he demands hard work. He is a big believer in the stats and running figures after each game.
"He demands hard work above everything else.
"In this division if you outrun the opposition - not just the general sense, but the high intensity - you generally come out with the points."