United were held to an eighth draw in 15 league games at Old Trafford on Saturday as they toiled against a disciplined and highly defensive approach from West Brom.
The 0-0 stalemate was United's eighth at home in the top flight since Alex Ferguson stepped down as manager in 2013, but Mourinho had already predicted on Friday that he would enjoy an easier second campaign in charge.
Pulis, too, thinks that United will be much improved next season.
"Jose is a top manager and it is a transition year for him," the West Brom manager told BBC Sport. "I would not bet against him winning the title next year. He will go out and get the players he wants."
Pulis also defended his own team's style of play on Saturday as they battled to a point, although he conceded they scarcely deserved anything more.
"If we won at the end, it would have been unjust." he said. "We are really pleased with the effort and commitment they put in today, United have some really good players.
"No matter how well set up you are, you will always be on your back foot. We have players who can do better in possession but it is a fabulous point to get at Old Trafford.
"The group plays very well together, they play very compact but we had opportunities to spring out of it like against Arsenal. Their resilience and commitment was fantastic.
"We did not want them in behind us and we did not want them to get us one-on-one. It was a really good team peformance."
And, while frustrated by United's failure to win the game, Mourinho agreed that he could not begrudge a visiting team being pleased with a point at Old Trafford.
"I'm not critical of it - they come for that, clearly," the United boss said. "If you ask Tony, for sure he will tell you that, but I'm not critical. One point is good for their objectives.
"They are solid in the table, they're trying to finish in the top 10. A point at Old Trafford is a positive for them."