Evans had been the subject of a bid from City during the transfer window, with Pulis confirming in August that a reported £18 million approach for the Northern Ireland international had been rejected.
Arsenal also came in for Evans and, had they met West Brom's price tag, Pulis suggested that they may have been tempted into a sale, despite the centre-half's importance to the club.
"It was very important we kept him,” Pulis said.
“Although the bottom line is that Man City and Arsenal 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.”
Though Pulis believes the former Manchester United defender would have been fine at a bigger club, thanks to his experiences at Old Trafford, he is happy to keep him aboard and hopes to he will sign a new deal.
However, the manager offered no promises of Evans keeping his place among greater competition.
"I'm pleased that Jonny stayed. He's a very down-to-earth lad, he's very level-headed,” Pulis said.
"He's been at 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.
"He has got to knuckle down now, get back in the team, and start showing everybody what a good player he is again.
"I hope we can offer him a new contract and tie him down, we will speak next week about what Jonny is thinking and what he wants to do."
Meanwhile, for Arsenal, missing out on Evans adds to a window that has been subject to much criticism.
While the Gunners did add Alexandre Lacazette, they missed out on Monaco’s Thomas Lemar after the player turned the club down and also sold Alex Oxlade-Chamberlain to Premier League rivals Liverpool.
Arsene Wenger also gambled on the futures of Alexis Sanchez and Mesut Ozil, who are both in the last year of their contracts. Sanchez was reportedly furious a move to Manchester City did not materialise, and Wenger has conceded it may cost up to £140 million for the Gunners when all is said and done.
Arsenal are in action Saturday against Bournemouth while Evans and West Brom face Brighton on the same day.