The FA Cup third-round tie marked the first anniversary of the death of 29-year-old midfielder Butcher from a heart condition, and Simpson, who had been assistant to former manager Alexander when he died aged 53 in 2010, said it had been an emotional day.
Simpson said: "Butch and the gaffer were a big part of this football club so it was a fitting way the lads went out and performed.
"Nobody would have been more proud of them than the gaffer and Butch."
David Wheater's late header rescued Bolton after Arnaud Mendy's spectacular volley had given the League Two side hope of an upset and a place in the fourth round.
Ivan Klasnic had given Owen Coyle's side an early lead, before Colin Daniel fired Macclesfield level and the Silkmen dominated much of the match until they ran out of steam.
Simpson added: "It was a good effort by us against the cream of our country - a team from the Premier League.
"We conceded early but we kept playing and took the game to them and got our rewards.
"It was a fantastic goal by Mendy - I didn't know he had that in his locker, what a great strike it was.
"He hasn't played a lot but I always thought that the kid would come to the fore.
"We hoped we could hold out but they are big, strong, and put the ball in the right area and always cause you a problem at set-pieces."
Simpson admitted the odds were against the Silkmen pulling off an upset at the Reebok Stadium but refused to give up hope.
He said: "I am a bit of a realist and usually the first bite of the cherry is the only one you get but we played quite well up there in the Carling Cup so we will give it another go."
Simpson also suggested that Wheater could have been sent off in the first half for pulling back Matthew Hamshaw.
"He was the last man so if that had us been pulling one of them back would he have gone? Let's leave it at that," said Simpson.
Bolton boss Coyle said he would not begrudge Macclesfield having a replay.
Coyle said: "All credit to Macclesfield, they are a decent side and they scored a truly magnificent goal.
"I've been on the other side many times as a giantkiller and you think 'that's a typical FA Cup moment'.
"But credit to the boys they kept going and it became waves of attack and we could easily have won, but I don't, and I don't think anyone would, begrudge Macclesfield being given another go at it."
Coyle dismissed suggestions that Wheater was fortunate not to be sent off.
He said: "It was in a wide area and there was Joe Riley and two or three players near him."
Gary Cahill was not in the squad for the match ahead of his expected move to Chelsea, and asked if the England defender would ever play again Bolton, Coyle said: "I'm not a party to the talks but if they conclude it then he won't, and if they don't then he will - it's very simple.
"We as a club have agreed a fee with Chelsea. I said to Gary and his representative to conclude that with Chelsea - if they do then great and if they don't he's a Bolton Wanderers player."
