The Eagles, who are 11th in the table, achieved their objective of survival in the top flight when they beat West Ham 1-0 last Saturday.
Pulis' side could still have a major influence on matters at both ends of the league, however, with Sunday's match against Manchester City coming before another home game against league leaders Liverpool and a visit to relegation-battling Fulham on the final day.
"We have a responsibility to the Barclays Premier League and to the rest of the teams that we give the best we possibly can," Pulis said.
"We know our two games at home are going to be very difficult against two top teams and Fulham might still be fighting to get out of the bottom three - other teams around us expect us to put in a shift so it's all to play for.
"I hope there won't be any let-up from the players.
"I think the fact they are big games, especially the two home games which are on television as well, gives the lads the opportunity to show everyone how well they've been playing and they have been playing well."
Marouane Chamakh and Kagisho Dikgacoi are both trying to shake off knocks as Crystal Palace host Manchester City in the Barclays Premier League on Sunday.
David Silva and winger Jesus Navas will both miss Manchester City's trip with ankle injuries, but Yaya Toure should be available again to bolster the midfield.
Toure suffered a muscle injury in the 3-2 defeat to Liverpool earlier this month but is now ready to return for the Blues.
Defender Matija Nastasic, out of action since February because of a knee injury, remains out.
Manchester City boss Manuel Pellegrini has said there has never been any concern that the club would be excluded from the Champions League for breaching UEFA's financial fair play (FFP) rules.
UEFA president Michel Platini has said he does not think any of the 20 clubs who are being investigated for breaches will be banned form European competition next season.
City have been working closely with UEFA to try to ensure they comply with spending rules, which limit losses to 45million euro (?37million) over the last two years.
Pellegrini said: "I felt here inside the club nobody feared we could be suspended for next year."
City insiders say they are confident that they will not face severe action from the European governing body
Any sanctions are likely to be made public at the end of next week.
Meanwhile, Pellegrini believes Sergio Aguero's return from injury could prove crucial as City try to push Liverpool all the way in the title race.
City travel to Crystal Palace on Sunday knowing that they must win if they are to have any chance of beating Liverpool to the league title.
Pellegrini said: "It is very good to have him back because I always say Sergio is a good player, he is important, he makes a difference
Always he is very important for the team."
Source : PA
Source: PA