While the Hoops are guaranteed to finish bottom of Group H, the Catalan side need a point to finish top the section after losing at Ajax in their last European game.
Barca have 10 points from five games with AC Milan second on eight points ahead of their game against Ajax, who are one point further back.
Martino, quoted on the club's official website, told a media conference: "This is an important game in all aspects - we have to finish top, we have to win and put in a good performance. For us, every game is tough and each one has consequences."
Barca scraped through 2-1 against Neil Lennon's side in their group game at the Nou Camp last year thanks to a last-gasp Jordi Alba goal.
And they were held for 75 minutes at Celtic Park earlier this season before Cesc Fabregas headed the only goal against a home side who had been reduced to 10 men following Scott Brown's kick at Neymar.
Martino said: "We have to be accurate and fast in our build up and in moving the ball around. We'll be playing in a 30-yard strip of pitch and we need to keep up the pressing too to stop Celtic hitting us on the break."
Midfielder Sergio Busquets warned the Scottish champions that Barca have "learnt our lesson from last year".
"They have their style of playing, which is very different from ours," he said.
"The sooner we get a goal, the better, because they can close down at the back and make it hard for us."
Busquets responded to questions about Barca's recent indifferent form, which has allowed Atletico Madrid to draw level with them at the top of La Liga and saw them lose to Ajax in their previous Champions League game.
He said: "The important thing for us is to win, but sometimes that isn't possible.
"Confidence is relative. We weren't good in Amsterdam, but defeats are a part of football and we have to show a reaction.
"We're not invincible and it's only normal to lose games during the season."
While Lionel Messi, Victor Valdes and Dani Alves are still sidelined, Xavi and Andres Iniesta will both be fit to face Celtic following injury as will Cristian Tello, although the Catalan club will be without the suspended Fabregas.
Martino said it would be "logical" for Neymar to start up front in the absence of Messi and Fabregas.