Crouch - who last played for his country in 2010 - scored both the Potters' goals in the clash at the Britannia Stadium to take his tally for the season to five in all competitions and earn the Staffordshire outfit their first win of the campaign.
Pulis said: "I'm not reluctant (to talk about Crouch and England), but Roy has a lot of experience and the last thing I want to do is tell him what team to pick. It has to be up to him. I don't think Peter can do any more than score goals and play well, and you have seen him today - in the first half he was unplayable."
Twice taking advantage of poor Swansea defending, Crouch headed home in the 12th minute and added a second nine minutes before the interval, tucking the ball away on the follow-up after Michel Vorm had parried his initial shot.
Reflecting on Stoke's display, Pulis said: "I thought in the first half we were very good. The worst thing that happened was half-time - we came out very slow and sloppy in the second half and Swansea controlled the play. But we got back into it in the last 20 minutes and I'm just disappointed Crouchy didn't get his hat-trick."
Having struggled in the first half, Swansea were better early on after the restart, although there was controversy in the 55th minute when their defender Ben Davies was booked for diving in the box.
"Simulation" had been a hot topic in the build-up to the game, with Pulis accusing Chelsea players of being guilty of it in Stoke's 1-0 defeat at Stamford Bridge last weekend and saying it was something that needed clamping down on.
Asked after Saturday's contest about the Davies incident, Swansea manager Michael Laudrup - whose side have now lost three league matches in a row - said: "From the bench it seemed like he was touched and that it was a penalty, but having seen it a couple of times more, I have more doubts.
"I don't think we have to go into arguing about whether it's a penalty or a yellow card. It can be in between - it is possible that it's not a penalty and you don't have to give a yellow card.
"In this case, the referee thinks Ben is trying to dive and gives him a yellow card. All I can say is that this is a 19-year-old boy and I don't think he has that in him. I don't think he tried to dive."
Source: PA
Source: PA