The Light Blues blew the chance to move 22 points clear at the top of the Irn-Bru Third Division when they were hit by a late sucker punch at Ibrox.
They now face one of their toughest games of the season when they travel to Tannadice next week for the fifth-round tie.
Templeton said: "If we do get chances like we did in this game, we have to take them.
"Dundee United are a strong side and we can't give them any chances near the end of the game because they will punish us.
"They've got some very good players, such as Johnny Russell, and if we give him any chances, I'm pretty sure he will punish us.
"We will have to be a lot better defensively and make sure we cut out our mistakes."
Much controversy has surrounded the United clash, after Rangers opted against taking their ticket allocation following calls for a boycott of the fixture by fans.
But, despite the setback against Montrose, Templeton says the challenge is one the players are relishing as they seek to replicate their impressive Scottish Communities League Cup win over Motherwell earlier in the season.
The winger added: "It's one all the boys are looking forward to.
"We will have to work hard this week and make sure we are ready for it.
"When Motherwell came here, it was one of the best performances we've had this season so hopefully we can step up and play better next week."
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