Wanderers took the lead inside the first minute at the Reebok Stadium through Kevin Davies, while Martin Petrov doubled their advantage in the 26th, firing in from just outside the area.
Bolton held out to set up a fourth-round home clash with Swansea a week on Saturday, and Coyle said: " We scored two good goals and created numerous chances to get other goals. But I think in the second half, if the truth be told - and I stressed this to the players - they probably felt it had gotten a bit too easy for them and that they knew they had won the game."
He added: "For me, you have to keep your foot down on the pedal, keep going and get those further goals. There were probably one or two thinking 'We have the game won, we have got Liverpool on Saturday and I'll try to keep a wee bit in the legs.'
"On balance, the most important thing is that we are through to the next round, but if you look at the game there is no doubt that we could have carried on in the vein from the first half and added further goals."
Macclesfield manager Gary Simpson was proud of his players' exploits, particularly after conceding the opener after just 34 seconds when Jonathan Bateson slipped when attempting a clearance to allow Ivan Klasnic to cross for Davies to score.
"It wasn't the greatest start in the world," Simpson said. "The kid has slipped and they punish you at this level when they get a chance.
"Going 1-0 down then we could have caved in, but we recouped a bit.
"We came in 2-0 down at half-time but we said if we could keep a clean sheet in the second half and put them under pressure at times, we might just nick one, and then we could take it from there.
"Credit to the lads, we have played Bolton three times now and usually if it is a League Two club against a Premier League club, 19 times out of 20 they will wipe the floor with you."
Source: PA
Source: PA