Bates has called for the whole squad to stay united during worrying times or risk enduring the reality of a second relegation in three seasons.
Despite a collective belief that Boro actually deserved something from the Ricoh Arena, the skipper was left having to come to terms with an eighth away defeat of the season.
Bates accepted responsibility for committing the rash foul on Gary McShefferey that gifted Marlon King the opportunity to score Coventry City's winner from the penalty spot, but feels there were enough reasons to be optimistic - provided they all stick together.
"There's a lot of things said in the dressing room after a match like that," he said. "We have to stick together because if we don't there is a chance we will be in the bottom three come the end of the season.
"It could be a dog fight at the end and we don't want to be in that. We have to regroup and if we keep playing like this we will get out of it.
"There's a realism in there. People know the situation and people aren't naïve, we know what is happening. It is important we stick together. We keep training well and we have to keep believing."
Bates was annoyed with himself for conceding the penalty 12 minutes from time that ultimately cost Middlesbrough a point at Coventry. The defender, however, insists it remains scoring goals that is the team's biggest problem.
Leroy Lita was guilty of missing a penalty and two fantastic chances to score, while Marvin Emnes hit the wood work and there were other opportunities for Middlesbrough to add to the four away goals they have scored in the league this season.
"We need to work on creating more chances. We did that on Saturday and the goals will come if we keep playing like that," said Bates. "We need to take heart from the performance rather than result. It was the best we have played this season. The gaffer's philosophies are rubbing off on us.
"It was a bad decision for me to go in for the tackle, that's football. But it was a good performance from us, we were the better team.
"Things are not going our way, you don't fancy penalties to go in because that is how things are going for us. Sometimes I have been sceptical of how we are playing and whether we are playing as well as we think we are, but we did play well. We can't keep getting results like we are. It is a bad situation, we can get out of this."
Bates, who retained the captaincy despite the return to fitness of Gary O'Neil, must now prepare for the visit of second place Cardiff knowing he will have a new partner at the heart of the defence.
David Wheater's fifth yellow card of the season - after an off the ball clash with McShefferey - has earned him a suspension, with Seb Hines the only fit centre-back left to select.