The Blades’ impressive early season form has been tempered by taking just one point from the last trio of games.
In all three – home defeats to Bury and Colchester United, plus Sunday’s draw at Bradford City –Nigel Adkins’s men fell behind.
Baxter, whose introduction during the second half at Valley Parade helped change the game, said: “We showed character at Bradford, most definitely. But we can’t afford to be going one or two goals down in every game.
“It is pressure we don’t need because teams like to sit in against us to try and make us do the work. If they get something to hold on to, then it just gets worse. We need to show more character straight from the first whistle, that is the aim.”
United host Doncaster Rovers this weekend and will be looking to take their performance in the final half-hour at Valley Parade into the derby clash.
Baxter did his hopes of starting no harm at all on Sunday by helping create Billy Sharp’s equaliser with a delightful through ball that opened up the Bradford defence.
He then followed that by heading off the United goal-line in the 95th minute as James Hanson looked set to snatch all three points for the Bantams.
“The pass was alright but Billy’s movement made my mind up to be fair,” said Baxter.
“The last thing you want is nobody in front of you moving. Once I got it on the half-turn, he made it easy.
“My clearance came from a bit of advice I got from Chris Morgan. He told me, once you see the ball go over your head, do whatever it takes to get back on the line.
“That is what you have got to do when you get a near post job. I heard (goalkeeper) Mark Howard shouting he had someone pinning him down and that a man had got away so that is what I did.
“You have got to stay switched on at all times because we want to be scoring, not conceding, last minute goals.”
The 2-2 draw at Bradford saw United move back up to seventh in the table after slipping down a few places the previous afternoon.
It remains, however, very tight near the top of League One – meaning a run to compare with the recent four-game winning burst could propel Adkins’ men much higher.
Baxter added: “Bradford are a great team with a good squad and some really good players on the bench.
“So, usually, you would walk away happy with a point. But with the expectations we have set ourselves and where we want to be, we were a bit disappointed.”