The Red Devils' win cuts City's lead at the top of the Premier League table to five points at least till the Pep Guardiola's side play at Huddersfield on Sunday. But the team created the chances to win and the possibility to score.
West Brom are seeking a new head coach after the dismissal of Tony Pulis last week.
"We moved the ball so slow in the first half hour", complained Pochettino.
When asked if the task of winning the Premier League is to great, Pochettino replied saying: "Yes, it's true. Only Harry (Kane) rescued one point but it is true our performance was enough to win but we didn't win".
The issue for Winks is that he benefits from playing against opponents who allow some space for him to showcase his impressive passing range.
The coach continued to BBC Sport: "I think we are disappointed because the effort from us was massive but we conceded the goal so early in the game, and they had the belief to play deep, so it was hard for us to move the ball".
Meanwhile, West Brom's interim boss, Gary Megson, was content with his sides toil: "Over the course of the ninety-minutes, obviously, a team of that statue is going to have a lot of possession at home".
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