Albion's head coach confirmed that Manchester City and Arsenal were both interested in his skipper, but failed to meet the club's valuation, believed to be north of £30million.
City had an £18m bid rejected, while Arsenal and Leicester City both had offers of £25m turned down.
Pulis doesn't believe that interest will have turned Evans's head, because he's already played for Manchester United.
But he has warned him that it may be difficult to get back into his unbeaten side now he's returned from his hamstring injury.
"It was very important to keep him," said Pulis. "The bottom line with Jonny is that Arsenal were interested and Man City were interested, they just never met the valuation the football club wanted.
"If they’d have met the valuation it might have been a different situation.
"I’m pleased that Jonny stayed. He’s got to knuckle down to get back into the team and start showing everyone how good a player he is again."
Pulis is confident the speculation hasn't affected his captain, who returned from international duty with Northern Ireland on Thursday.
Evans was believed to be keen on a move to City, but Pulis reckons the 29-year-old's stint at Manchester United earlier in his career will help soften the blow because he's already played for a top-four club.
"He’s a very down to Earth lad," said Pulis. "He’s very level-headed. He’s been one of the great clubs in world football for a long time so going to Man City or going to Arsenal would not have fazed him at all. And I don’t think the speculation fazed him."
Alongside Ben Foster, Evans has been Albion's most consistent performer over the past two seasons. But he missed the first four games of the season with a hamstring problem, forcing Pulis to play Ahmed Hegazi and Craig Dawson at centre-back. The pair have only conceded one league goal so far this season and Pulis hasn't guaranteed Evans a place in his team.
"We've had a look at him in training after he played two games in quick succession for Northern Ireland," said Pulis. "But Dawson and Hegazi have done very well in the four games they've played."