The England international struck his seventh goal in nine league games to move the champions on to 40 points, nine clear of the relegation zone.
Shakespeare has been thrilled with Vardy's recent performances and wants him to score as many as possible to make Leicester's safety mathematically secure over their final four matches.
"I think strikers can have that rich vein of form," he told BBC Sport. "I want him to finish on a high. He's scored quite a few of late and we need that to continue."
Leicester have taken 19 points from a possible 27 since Shakespeare replaced Claudio Ranieri as manager but the 53-year-old said the praise must go to his team.
"Ultimately it's about the players. I can pick the team and the tactics but they've got to perform. Great credit goes to them," he said.
"I'm just pleased with our performance. We showed different aspects today, we had to defend... it was a gutsy performance and I'm really pleased with the three points.
"We'll sit down and reflect at the end of the season. I can reflect personally as well but we need to get to the end of the season."
3 - Jamie Vardy has scored in all three of his Premier League appearances away at West Bromwich Albion. Thorn.— OptaJoe (@OptaJoe) April 29, 2017
The result made it four defeats in a row and no goals scored in five games for West Brom, who had the greater chances on Saturday but succumbed to Leicester's only shot on target.
Boss Tony Pulis was frustrated at the manner in which they conceded but insisted that a stroke of luck is all they need to get back on track.
"I don't think we deserved to lose. It was a poor goal we conceded. Vardy scores those goals all the time and we talked about not leaving space behind us on the changeover," he said.
"We had opportunities and the lads worked really hard. They had one chance and Vardy stuck it away.
"It's not as though the players have packed it in. We need a break and we're not getting it.
"You've seen the players running around today. It's the fourth game we've lost 1-0 and we could easily have won or drawn them."