Glenn Murray and Marouane Chamakh scored for the Premier League side, but it was the second-tier hosts who sealed victory courtesy of debutant Moses Odubajo.
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"We have been to Austria and America and only returned on Thursday morning from a long round trip to the States," he told the club's official website.
"A few of the lads felt a bit leggy going into this one, but I kept all the outfield players on and it proved useful for the lads.
"The game got stretched which, again, was good for us. It was end-to-end stuff and I thought our boys worked their socks off today. It was a really good game for them to be involved.
"It was really important for them to come through like they did. The lads worked really hard and can be pleased with their efforts."
Pulis transformed Palace's fortunes when he took over in November last year, guiding them comfortably to top-flight safety and he will seek to build on that progress this term - but ruled out making a host of signings.
"The window doesn't close till the end of the month so we've still got plenty of time," he added. "I won't be signing a large number of players like the club did last year on the final day of the window."