Rory Best was disappointed to see Ireland allow Wales a way back into their Six Nations opener having initially raced into a 13-0 lead.
Ireland were quick out of the blocks at the Aviva Stadium, but a Taulupe Faletau try helped Wales reduce the deficit to just three points by the break.
Rhys Priestland kicked Wales in front late in the second half, but Jonathan Sexton ensured the spoils were shared at 16-16 with one last penalty.
"A draw is a hard result to put into words," Best, who has taken over from the retired Paul O'Connell as captain, told ITV. "We're happy we didn't lose the game.
"After going behind for the first time with six minutes or so remaining, we showed great character to come back and get the draw.
"That's the positive and we have a lot of work-ons to work on.
"We wanted to start well, because with the way Wales defend it is a hard task to get back on top of them if they go ahead.
"When we got the ball in the opening half hour, we looked dangerous so it was pleasing. To let them find a way back is a bit disappointing."
Ireland head to Paris to face France on Saturday.