In a statement on the clubs official website, Stewart urged everyone to try and pull in the same positive direction for the final run in.
"Having seen and heard certain comments and speculation since Saturday's game I think we all just need to take a deep breath and take stock on our position," insisted Mr Stewart.
"We are coming towards the end of the season and we all feel the tension, we all get the nerves, but I think we just need to put some realistic perspective on our position and if people think that we sit back and that the manager, the staff, the Board and, especially the squad of players, are all satisfied with the current level of performance and run of results they are very much mistaken.
"We all know that the current squad are capable of performing to a level that will match or beat any side in league two, so let's get behind this team and encourage the team and the manager to excel in this time of need and high expectations.
"Look at Portsmouth's spirit yesterday - against all odds and against all the form guides, they were so solid and together as a unit and did the manager, the supporters and the name of Portsmouth Football Club proud," added the Chairman.
"We just need to galvanise our spirits and stick together, at Rotherham United Football Club we have come a long way in a short space of time and, let me promise you this, we will continue to make progress in all areas, and we will not stop our unrelenting approach to progress in every single area for this Club.
"God bless you all for your support."