The Potters came from behind to win 2-1 against Besiktas at the Britannia Stadium on Thursday night, and following their 1-1 draw at Dynamo Kiev a fortnight ago, Pulis' men now lead Group E after two rounds of fixtures.
"There are only two games gone, so lets see where we are after six," the Welshman said. "We've got to try to win our home games - that is very important, and it is a good start against a very good side."
Pulis was delighted to see Stoke overcome their Turkish opponents, who he views as a "massive danger" in their group.
Besiktas went ahead just before the quarter hour mark when Roberto Hilbert struck into the far corner having latched on to Ricardo Quaresma's pass, but their lead lasted only a minute, goalkeeper Rustu Recber unable to claim Dean Whitehead's corner and Peter Crouch on hand to bundle the ball over the line.
The two sides, roared on by their equally-vociferous sets of fans, played out an entertaining contest from there, with both hitting the woodwork. Substitute Jon Walters then settled things in the 78th minute, hammering a penalty past Rustu after Crouch had been brought down by Tomas Sivok.
Pulis had been to Istanbul on Sunday to watch Besiktas play and knew they were always going to pose a threat.
"They have some good players, and some of them that played here had been rested on Sunday," Pulis said. "We think they are a massive danger in this group, so we are very pleased with the result.
"I thought in the first half in patches they played very well, outnumbered us in midfield and moved the ball very quickly. At times we were chasing the ball.
"But in the second half we made some changes, pushed on a bit and caused them a few more problems. On another day we could have scored three or four goals."
Source: PA
Source: PA