Debut goals from Grant Holt and Leon Barnett, sandwiched between strikes from Ben Watson and Shaun Maloney, gave the Latics a comprehensive victory at Oakwell.
Barnsley, who were second best throughout, played the final 25 minutes a man light after substitute Dale Jennings was dismissed five minutes into his debut.
"I think if someone had told me before the game that the performance was going to be of that stature, then we'd have grabbed that with both hands," Coyle said.
"I stressed to the players before the game, and I'll stress it after the game, anybody who comes to Barnsley and thinks they're going to walk in and be handed anything then they're sadly mistaken. They're going to have to put in big performances to win points here, there's no doubt about that.
"We knew in the early part of the game we were going to have to stand toe-to-toe with them and earn the right to play our football, which we did. It was ever so pleasing.
"We scored four goals and, if truth be told, we could have had few more. But it's one game and there's 45 to come and we're certainly not getting carried away in terms of what it means. It means three points."
Watson smashed the visitors ahead with a 25-yard drive eight minutes before the break before Holt touched in Emmerson Boyce's effort in the 54th minute.
Jennings was sent off on the hour mark for a lunge at James McCarthy and the Latics made the most of their numerical advantage as Barnett and Maloney both finished from close range late on to give Wigan a fantastic start.
Barnsley boss Flitcroft felt his team were outclassed as he endured an afternoon to forget in his first game in permanent charge of the Tykes.
The home side failed to muster a meaningful attempt on goal as they were beaten convincingly and the Yorkshire side's day was compounded by the sending-off of debutant Jennings.
"I thought Wigan were devastating," Flitcroft said. "I thought up to the goal going in, we probably had our best spell. I thought we gave them some problems for 10 or 15 minutes of the first half, I really did.
"It was quite a competitive first half and we had a bit of possession, but once the first goal went in we struggled to come to terms with that.
"The second goal after half-time deflated the team and then when Dale (Jennings) was sent off then you're chasing Wigan with 10 men, and it hurts at times watching your team having to endure that.
"I don't think as a group they deserved that to happen to them, but it did and we'll grow strong from it.
"We've been well-beaten today but there are still a lot of points to play for.
"I think Wigan have put a bit of a benchmark down today and I've told the players if you want to emulate that, then there's a lot more work we've got to do together, and we'll continue to do that."