The Merseyside club are fifth in the table and still harbour hopes of securing a place in next season's UEFA Champions League.
They cut the gap to fourth-placed Arsenal to eight points with a pulsating 3-2 home victory over Swansea City on Saturday as Arsene Wenger's side slumped to a 6-0 defeat at London rivals Chelsea.
Martinez's charges also have a game in hand over Arsenal as they prepare to travel to Newcastle United on Tuesday and the Spaniard is eager to ensure that his players do not waste the opportunity in front of them.
"We're in a very, very good moment," he said after the weekend win.
"Players are fresh, looking forward to every game. We've got nine games to go and we need to make sure that we take advantage of every single point that we can get."
The stadium ban handed out to boss Alan Pardew following his headbutt on Hull City's David Meyler did little to hamper them on Saturday as they left it late to beat Crystal Palace 1-0 at St James' Park.
Papiss Cisse's injury-time strike gave them all three points to move them up to eighth, with assistant John Carver masterminding things from the dugout in Pardew's absence.
That strike marked a first goal in more than two months for Senegal forward Cisse, and captain Fabricio Coloccini hopes he can now kick on from here.
"We are all so happy for him because strikers live to score and he has been a bit unlucky in the last few games," Coloccini told Newcastle's official website.
"He had a few chances (against Palace), which their goalkeeper saved, and then missed one from Mapou (Yanga-Mbwia's) cross but he never gave up and hopefully this gives him a lot of confidence."
The absence of injured top scorer Loic Remy, who will miss out again with a calf injury, could hamper Newcastle - and they will also be missing full-back Mathieu Debuchy with a groin complaint.
