City had two offers rejected by the Baggies for Evans, 29, while Arsenal were also interested in the former Manchester United centre-back and had an approach turned down.
Pulis insisted that the decision not to sell the Northern Ireland international was the right one and added that the situation was less complicated than it could have been as the player did not agitate for a transfer.
"We're pleased that value is that value, and I'm even more pleased we never took [any bid]," Pulis was quoted as saying by Press Association Sport before West Brom's Carabao Cup clash against City on 20 September.
"You heard about Jonny more because it was the bigger clubs after him. You have to manage it.
"It is not easy and you have to manage it within the group because there are a lot more players. It's important you keep all that together.
"I think he said he was a West Brom player until anything changed and he's remained a West Brom player, thank goodness. We move on with it now and we'll march forward."
A product of Manchester United's academy, Evans spent nine years in the first-team at Old Trafford before joining West Brom in 2015.
He started 31 league games for the Baggies last season and was made club captain by Pulis this summer following the departure of Darren Fletcher to Stoke City.
"I think he's done well here in lots of respects," Pulis said. "He's become a better defender. He's always technically been a good centre-half, but he now has the responsibility of being captain will take him on again.
"He's a very fit lad and Jonny has got a lot more in the tank. He's a lad who could play well into his thirties."