Sunderland looked to be heading for an opening-weekend victory when Jack Clarke headed home Lynden Gooch's cross to open the scoring in the 12th minute at the Stadium of Light.
The Black Cats soaked up Coventry pressure, with Anthony Patterson producing a superb save as he tipped Jonathan Panzo's long-range strike onto the crossbar, but their hopes of claiming all three points disappeared when Gyokeres struck with six minutes remaining.
The Sweden international swerved past two defenders before hammering a superb strike into the bottom right-hand corner, and, having guided his side to promotion via the play-offs last season, Neil admits you do not encounter a similar standard of opponent in League One.
The Sunderland boss said: "I thought we gave a good account of ourselves. I thought we were organised, and we made it really difficult for them. Let's be honest, we'd be talking about a great result here if it wasn't for one moment of quality.
"We switch off, don't get down the line quick enough and let him turn, but even then, it's a great goal. It's not as if we've made an error and they've had a tap in. The lad's had to turn, dip past two players and bang the ball in the bottom corner. That's the quality of the Championship."
Nevertheless, Neil was happy with his players' efforts as Sunderland returned to the second tier after a four-year absence, with Coventry goalkeeper Simon Moore making a fine second-half save from Ross Stewart.
He said: "You don't know how players are going to react. We've still got a lot of work to do in the window in terms of strengthening the squad, but I thought we moved the ball really well and probably caught Coventry a bit cold in terms of how we started the game. All in all, for what our players offered up, I was really pleased with our effort and how we went about it."
Coventry boss Mark Robins admitted his side were punished for a slow start, but felt a draw was the right result given the way in which they stepped things up after the interval.
He said: "Any point in the Championship is a good point. It's a tough place to come, especially in the circumstances with it being their first game back in the Championship after four years away.
"I'll take a point and move on. The change we made gave us a leg up and gave us a bit of impetus in the game. We added a bit of pace and managed to create one or two things, then we got the goal through Vik. Then we looked like we could build that pressure to go on and get another one.
"We had to do better, and I thought we started to do a bit better in the second half. The change in shape and personnel did the trick in terms of opening them up a little bit more. We've got more options once we get up to speed now."