The Blades fell behind in the first-half courtesy of a stunning curling effort from Birmingham winger Jeremie Boga. However, they once again showed their character in the second-half to fight their way back into the match through Leon Clarke and could have even gone on to secure all three points.
Wilder felt that there was only ever one team which was going to go on and win the game. He said: "I do not think we deserved to draw the game but credit to the opposition. They defended fantastically well, we pushed them back for long periods, we just could not find a winner."
He added: "We are up against big clubs in this division, big teams, good players. (They have) a good manager with experience and they have had to work extremely hard to get a point."
Blades concede another wonder goal at Bramall Lane
17-year-old Fulham winger Ryan Sessegnon scored a stunning goal on his way to a hat-trick in their 5-4 win against the Blades on Tuesday night and United conceded another wonder goal against the Blues. However, Wilder does believe his side could have done more to prevent Boga's effort from finding the back of the net.
He said: "Small criticism (is) that we should have got out to him a little bit quicker but it is another fantastic strike. Sessegnon scored one on Tuesday night from a similar position. They (then) got men behind the ball and made it extremely difficult for us but I am delighted with the way we are playing."
Wilder did acknowledge the contribution of in-form striker Clarke as he bagged his 13th goal of the season against the Blues but was also quick to point out that his entire team is performing to a high standard on a regular basis.
He said: "He led the line well. He has been outstanding but I thought all the performance levels of all the players were up there and they have been all season. They are consistently producing performances of a high level in a tough and competitive league."
He added: "We have got no right to be in the position we are in. Absolutely no right. We are defying the odds, we are enjoying it, the club is enjoying being in The Championship. It was a big afternoon for us to see what our reaction would be like after Tuesday night."
Wilder believes his side deserved more
The Blades have been very consistent this season, especially at Bramall Lane. This has resulted in disappointment in the dressing room that they only managed to pick up one point from two home games this week. However, Wilder believes the results will continue to come if his side continues to perform at such a high standard.
He said: "We are disappointed because we have had two homes games and we have been fantastic at home but only picked one point up. Maybe we deserved a little bit more today. There are a lot of really disappointed players in there (dressing room). We have come a long way and we do not want it to stop."
He added: "I think it would have been unjust if they had won the game. They wanted to get a result for their football club."
United will be eager to get back to winning ways next weekend when they travel to The New Den to take on Millwall. Wilder will be aware that his side will need to secure the three points if they are to keep up with the likes of Wolverhampton Wanderers and Cardiff City who currently occupy the automatic promotion places.