The Latics' 3-1 win over the Slovenian side in the DW Stadium's first European game was their maiden victory in continental competition.
Powell profited from a goalkeeping howler to become the first Wigan player to score in the Europa League and FA Cup hero Ben Watson made it two before half-time.
Tavares took advantage of profligacy from Powell to pull one back and would have levelled matters in the 90th minute but for a stunning save from Scott Carson.
But a fine individual goal from 19-year-old Powell wrapped up the points to put Wigan second in Group D.
Powell joined United in 2012 from boyhood club Crewe and scored on his Premier League debut against Wigan last September.
His loan spell with the Latics runs until the end of the season, and Coyle believes he has the potential to follow in the footsteps of two other young players he has helped move forward in their careers.
Coyle said of Powell: "That's why we brought him here because I believe he's a top player in the making and nights like this will certainly help.
"He's got so much to offer. I want it on a consistent basis, and I'm trying to demand that of him to help him progress his career.
"I've been fortunate to be able to do that before with a couple of very good players and I see Nick Powell in that category.
"To do that he's got to bring performances like this on a consistent basis and show that after his year's loan, when he goes back to Manchester United, that he's in a position to challenge for their first team.
"And if he is, given the level they play at, that would then push him towards the England limelight. He's a bit off that yet but he's certainly got the ingredients that we can help to move him forward."
Powell is more comfortable in midfield but injuries to Grant Holt and Marc-Antoine Fortune meant he was pushed into a striking role, and he could easily have had five or six goals.
Coyle was delighted to see his side acquit themselves so well at a new level.
"When we bring it all together, it's a terrific sight to see, and you saw that here," said the Scot.
"Sixteen years ago we were a Division Four club and to be out there on that European stage - and not only on the stage but showing the quality they did. Because with that performance, we would have stood toe-to-toe with an awful lot of teams, and that was very pleasing."