The Blues had taken the lead in the first-half courtesy of a superb curling strike from winger Jeremie Boga. However, they were unable to hold out until full-time as Leon Clarke grabbed an equaliser for the Blades around 20 minutes from time. The Blues then had to survive a late onslaught from the home side to ensure they came away with a point.
Cotterill was pleased with his side's result. He said: "It was a good point. I think had we scored the second one, I think we would have won the game."
He added: "Sheffield United are on a great run of form, have got a good team spirit about them, way of playing which will always be a success if you have got that in your football club. (It is a) tough place to come, big crowd, so a really good point for us in the end."
Boga performs on rare start for the Blues
Cotterill opted to include Boga in his starting line-up, despite the fact that he has rarely featured from the start since he took over from Harry Redknapp. However, Boga proved that he is worthy of a starting place on a more regular basis with a stunning goal to open the scoring in the first-half.
Cotterill described Boga's strike as an "absolute screamer" but explained that he had not produced this enough in training which is "why he has not been picked" in the starting line-up much in recent weeks.
He said: "It was pleasing for Jeremie. He is a really nice lad. Unfortunately, just before I had taken the job I watched him at Hull (City) and I saw him playing on the left wing that day and I did not see too much to encourage me. I have to be honest with that. I thought let’s have a look at him as a striker."
He added: "Jeremie is a wide left player who has ended up playing upfront. Sam Gallagher is a striker who has ended up playing wide left. They actually looked better suited in those positions. By flipping them, it has given us better options."
Cotterill rues a tough turnaround following midweek fixtures
Cotterill was left delighted with his side's efforts after two tough away games in the space of a couple of days. Birmingham fell to a 2-0 defeat to Middlesbrough at the Riverside on Wednesday night, leaving them little time to prepare for this one.
He said: "(I am) delighted for Jeremie, delighted for the boys. (It was) a quick turnaround from Wednesday. You do not really want to be coming here when Sheffield United have had a game on Tuesday and an extra day’s preparation."
He added: "By the time we got back from Middlesbrough it was about 3am so that makes Thursday a washout. It has been hard but the boys have been very receptive but it was a tough turnaround for us."
Cotterill was left "slightly disappointed" with the manner in which the Blades scored their equaliser as he felt that there was a foul on Lucas Jutkiewicz in the build-up.
He remains acutely aware of the position Birmingham find themselves in towards the bottom of the Championship table and knows exactly what is required if the Blues are to secure safety. He said: "No matter how many times you get punched in the nose you have just got to keep on moving forward with it and carry on working hard on the training ground."
The fixtures get no easier for Cotterill's side as they face local rivals Wolverhampton Wanderers at St Andrew's next weekend. However, the Blues will be boosted by the return to fitness of striker Che Adams who came off the bench against the Blades in the latter stages.
Cotterill believes Adams will be ready to face the current Championship leaders next weekend. He said: "He has done very light training to sort of test it. Perhaps it was not as bad as we thought it was. We have managed to get him on the bench, training next week, strengthening again and he should be ok and available for Wolves. All of it is a bit of a risk at the moment."