The Terrors thrashed St Johnstone 4-0 in the Premiership at the weekend but with one eye on Saturday's visit of Celtic, McManamara is expected to rotate his squad.
Nadir Ciftci is among those players hoping for a start but Gavin Gunning remains suspended so Keith Watson could keep his place for the second-round clash.
"We can't rely just on the same 11 guys each week," McNamara said.
"Those who come in will be able to do a good job and I want the players to be pushing each other at every opportunity.
"Dumbarton is a hard place to go so we won't be taking it lightly. We have to show the same application and desire as we did at the weekend against St Johnstone.
"That was a real confidence booster for the lads and everyone played their part."
Championship side Dumbarton have been buoyed by a 3-1 win over Greenock Morton and Colin Nish, who made one and scored one on his debut, is set to spearhead their attack.
"United are a quality team and their 4-0 win against St Johnstone shows just exactly what we will be facing," Sons boss Ian Murray said.
"Obviously we'll be underdogs, but the game will be played at our place so that should give us a wee edge."