The Londoners kept pace with the division's leading pack courtesy of Wednesday's 4-0 win at Newcastle United, sealed by Emmanuel Adebayor's double and further efforts from Paulinho and Nacer Chadli.
Liverpool's dramatic win at Fulham keeps Shrewood's side three points off a UEFA Champions League qualifying place, and a poor goal difference - 30 behind the Merseyside club's - does nothing to help their cause.
With games against Chelsea and Arsenal, as well as Liverpool, still to come, Sherwood is expecting the race for a spot at Europe's top table to be a thriller.
"It's going to go down to the wire," he said. "It's going to be tough to maintain a run.
"Liverpool are doing excellent and we just have to make sure we keep breathing down their necks.
"If we prepare ourselves correctly and work to our gameplan, with the players that we have it should come off."
Sherwood reserved special praise for double scorer Adebayor, who has now netted eight times in 11 games since being brought in from the cold after Andre Villas-Boas' departure.
The Togo striker's work-rate has been questioned in the past, but Sherwood insists that he is one of the hardest workers in his squad.
"I always ask Adebayor for more, at the moment he's at the top of his game, he's an example to all our young players," Sherwood added.
"He's someone who applies himself on and off the pitch. He works real hard in training, never leaves anything on the training pitch and he mirrors that on the field."
