McInnes and assistant Tony Docherty left the Pittodrie club earlier in the week, with their eight-year spell in charge coming to an end following a goalless draw at home to Hamilton.
Sheerin, Barry Robson and Neil Simpson have stepped up as the interim management team and the former Arbroath manager spoke to Aberdeen's official website about a "subdued week" before revealing the aim of unity.
He said: "The players have built up relationships with Derek and Tony over the years, they signed almost every single one of them. From that point of view, it is tough, but all of the players will pull together.
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How the Hearts players rated in the draw against Hibs
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"The staff will all pull together. Everybody wants what is best for the club, and that is what we want to achieve.
"We won't be making any hugely dramatic changes. We know what we need to do.
"We will continue to strive to be better and break this duck and start scoring goals. It is obviously important, you need it to win games, that is stating the obvious.
"There won't be wholesale changes in the way that we approach things and we have mentioned that to the players.
"Hopefully they will be responsive to the little things that we do change. It is a case of reminding the players that they are still good players. "
Sheerin, who stepped up from reserve team coach, outlined his ambitions for the club before the end of the season, one of which is to overcome Hibs
He said: "We are three points behind Hibs and we still have a Scottish Cup to compete for.
"There is still a massive part of the season to play for and a lot to look forward to.
"For whatever period that myself and Barry are in the job, we will do all we can to try and deliver third spot and get a run in the Scottish Cup.
"We will keep the standards that Derek and Tony have set and hopefully results will turn.
"I think third spot is still achievable, it is in Hibs' hands and it is going to be difficult, there is no getting away from that but there are still enough games left in the season."