The manager had imposed an alcohol ban after his side’s midweek 6-0 victory at Bradford had made sure of Championship football next season.
But after seeing his club earn their first title success in 60 years, Cotterill said: “I won’t be anywhere near the players. They can let their hair down.
“We would all have liked a drink after the Bradford game, but there was still a job to be done because we desperately wanted the silverware.
“So it was tea and orange juice on the coach coming home. Now I might have two cups of tea and I’m expecting a free coffee at my local Costa (on Sunday)!”
Cotterill added: “It was great to share our success with our fantastic supporters at the end.
“They have been through some tough times, but this club has the potential to reach the Premier League if everything falls into place.”
A point from a closely-fought game was enough to guarantee Bristol top spot, while for Coventry it represented another step towards safety.
Home defender Derrick Williams wasted the best of few clear chances when heading over from Luke Freeman’s 11th-minute corner.
But Coventry were lively going forward and Frank Fielding had to produce a fine diving save to keep out John Fleck’s 36th-minute volley from the edge of the box.
Bristol felt they should have had a penalty in the closing moments of the first half as Kieran Agard went down under a challenge from the imposing Reda Johnson.
A low-key second half saw Freeman fire wide for the home side, while Nick Proschwitz almost grabbed all three points for Coventry in injury time, narrowly missing the target from inside the box.
Coventry boss Tony Mowbray was generous in praise of Cotterill’s men.
He said: “We have come to the best team in the league and almost done enough to nick all three points.
“All credit to Steve for winning promotion by playing positive attacking football.
“They deserve to be champions, while we still have work to do to make sure of staying in the division.
“We managed to restrict them without being defensive and had chances to win the game.
“We have been pretty good away from home in recent weeks and it’s another performance to build on.
“The lads are disappointed in the dressing room because a few shots flashed wide or brought good saves.
“It was a difficult game for Bristol emotionally and we had to do our best to capitalise.”
A minor pitch invasion at the final whistle was soon cleared and Cotterill had nothing but praise for the club’s partying supporters.