The FA Cup third-round tie marked the first anniversary of the death of 29-year-old Butcher from a heart condition, and Simpson, who had been assistant to 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."
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.
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."
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."
Source: PA
Source: PA