Rory Fallon's brilliant volley gave the Pittodrie side the lead they deserved before Paul Heffernan got Kilmarnock back on terms five minutes before half-time.
Boyd has penned a deal until the end of the season with Killie and Shiels expressed his delight at completing the move.
"The signing had an effect as Heffernan and (Jamie) Langfield were outstanding," said Shiels.
"He's made a major contribution to this club and is a legend here - it's great to have a player like that here.
"Aberdeen have quality right through their team, I think after they enjoyed the better of the first 20 minutes and hit the post, that could have killed it off. But we dug in, made some chances and then got the goal we deserved.
"The first 20 minutes of the second half we were bossing it and then Aberdeen started hitting us on the break."
Shiels refused to comment on the penalty claim for Aberdeen in the second half - the Rugby Park manager's outspoken nature has landed him numerous touchline bans this season.
Diplomatically, he said: "If I talk about referees and penalties then I could be penalised - I'm going through a self-discipline programme at the moment to try to stay away from the truth as much as I can."