Rovers nearly spoiled the party in Coyle's first home game in charge thanks to first-half goals from Theo Robinson and Chris Brown.
Wigan's eight-year stint in the top flight ended last season and Coyle believes the current squad must switch their mindset when they fall behind now they are frequently expected to win games.
"When all too often in the Premier League you've been second favourites and you lose a goal against a quality team there's a tendency to think you might not get back into it," said Coyle.
"What we've got to understand is even when that happens to ourselves in the Championship, we've got enough quality at any given time to come back in any game against any opposition and I felt the reaction wasn't good enough."
Despite that, Wigan's ability to salvage a draw in the second half pleased Coyle, who added: "When we came in at half-time there was certainly one or two words spoken.
"The character, the resolve, the desire, everything I ask of teams of mine was there in abundance.
"The spirit they showed, the desire, the work-rate for each other in the second half is very pleasing. Obviously we need to make sure we're not giving teams two-goal head-starts but there were a lot of positives to take."
The outcome could have been entirely different too had the hosts been awarded a 15th-minute penalty when Grant Holt was hauled down by Reece Wabara right in front of goal.
"I've seen it back and it's the biggest stonewall penalty you'll ever see in your life," said Coyle.
"Grant's a yard in front of the lad and the lad's just dragged him to the ground. I've got no doubts if we had gone that goal in front tonight we'd have gone on to win that game with a couple of goals to spare.
"But, fair play to Doncaster, they got a 2-0 lead... second half it was like that old movie 'The Alamo'. It was waves of attack, we kept coming and coming and it's a great characteristic to have in your team."
Doncaster boss Paul Dickov was delighted to earn a share of the spoils against the FA Cup holders, although he acknowledged Rovers' misfortune with both Bongani Khumalo and Billy Paynter hitting the woodwork.
"To come here against a team that I consider one of the best if not the best squad in the division and compete the way we did and get a point is really pleasing," said Dickov.
"At 2-0 we've hit the bar which was a massive turning point in the game because at 3-0 it's possibly a lot harder for them to come back, even with the quality they've got.
"Obviously they get back to 2-2 and you're thinking about hanging on and Billy has a fantastic header that comes back off the bar as well, so I suppose it was an exciting game for people to watch."
- Sports & Recreation