Fifth-placed United are in their fourth season in League One and a last gasp 2-1 defeat against lowly Crewe Alexandra left them just five points clear of a trio of teams outside the play-offs.
Barnsley, who are unbeaten in nine league matches, are among that group and can close the gap at Oakwell.
But United manager Clough is urging his team to stay relaxed in their pursuit of the Championship.
"Everyone is desperate to go up but that needs to come across in the right way," Clough told BBC Radio Sheffield.
"There's no point in us panicking or the players panicking. We have to stay calm and relaxed and play our football.
"We're still in a great position and reaching the play-offs is in our hands."
Saturday sees another important game in the race for promotion with third-placed Swindon Town playing host to MK Dons, who are a place and a point behind Mark Cooper's men.
Preston North End are in second and will hope to put some distance between themselves and the chasing pack by beating a Rochdale side who only a point behind the top six at Deepdale on Friday,
Simon Grayson's side have not lost a league match since January, but back-to-back draws have left Swindon and MK Dons breathing down their necks.
Leaders Bristol City will look to take another step towards what is becoming a seemingly inevitable promotion to the Championship by winning at Oldham Athletic, while play-off hopefuls Chesterfield and Peterborough United visit rock-bottom Yeovil Town and strugglers Scunthorpe United respectively.
Colchester United, who are 23rd, are in danger of being cut adrift and seek a much-needed three points at Port Vale, while Crewe and Crawley Town meet in a relegation six-pointer at Gresty Road.
Notts County are outside the relegation zone on goal difference only and face a difficult trip to Walsall.
In other matches, Bradford City make the short trip to Yorkshire rivals Doncaster Rovers and Gillingham welcome Fleetwood Town.
