Danny Wilson felt Sheffield United deserved their place in the third round of the FA Cup after their 2-1 home win over Port Vale.
Tom Pope had given the visitors a 33rd-minute lead with his 21st goal of the season but Shaun Miller equalised in the 90th minute before then firing a winner deep into stoppage time at Bramall Lane on Saturday.
Wilson said: "It was quite a big relief in the end to get the two late goals. I thought we put them under extreme pressure in the second half. We faced another 'keeper again who's been in inspired form (Chris Neal) and there were also some glaring misses from our perspective.
"We persevered and we got that all-important equaliser. We felt that in the minutes that were left we'd get the winner. We didn't sit back. We went for the throat and thankfully we got the goal.
"Shaun (Miller) is a goalscorer. There are parts of his game he can improve, and that goes for most players, but what he's got an eye for is a goal. He'll be disappointed that he didn't get a goal before he actually scored because he had a couple of good chances.
"He persevered and like all good strikers he didn't get disappointed and kept getting in key areas and thankfully a couple dropped to him."