Rangers cut the gap to a still daunting nine points between themselves and Aberdeen following a comprehensive 3-0 win last Sunday.
Rangers have had a disappointing campaign on their return to the Scottish Premiership with bitter Old Firm rivals Celtic running away with the title, wrapping it up with eight games to spare.
However, Waghorn says last week's win will give Rangers renewed hope as they target the runners-up spot in the Scottish Premiership and a Scottish Cup semi-final win over Celtic next week.
"We have a few big weeks ahead of us and it's important that we build on the result and we want another win at the weekend to set us in good stead for the upcoming Cup game," said Waghorn, whose side host Partick Thistle on Saturday.
"We want to finish as high as we can in the league. We can't rest on our laurels, we want to finish the season as best as we can.
"You've got to aim as high as you can and it's definitely in our sights to go and get second place and weâre going the best we can to do that."
'It's been a good challenge'
The Rangers striker also revealed new manager Pedro Caixinhaâs meticulous preparation and strict training regime is proving a hit with his players.
The Portuguese has introduced a new six day training schedule for the players since his arrival last month.
The 46-year-old has had a mixed start to his tenure with disappointing draws against Motherwell and Kilmarnock bookended by emphatic wins over Hamilton and Aberdeen.
But Waghorn says the whole squad is now benefitting from the high intensity training put in place by Caixinha as they prepare to take on a Partick side unbeaten in their past eight league matches.
"The training methods, the style he wants us to approach games, the analysis of other teams, it's all been different to what we are used to," the 27-year-old former England Under-21 international said.
"But it's been a good challenge and all of the boys are enjoying it. Hopefully, that's shown in the results on the pitch."
Elsewhere, champions Celtic travel to take on Ross County on Sunday.
Celtic manager Brendan Rodgers says while he may make changes to his side -- who are unbeaten in 39 domestic matches since the beginning of the season -- he will still pick a strong team with the Scottish Cup semi-final against Rangers in mind.
"Between now and the end of the campaign, some of the players who have been on the outside will get some games and it's a chance to give one or two with knocks the right preparation," he said.
"There will be some changes through the course of the season, but I don't give up places just for the sake of it."
Fixtures (1400GMT unless otherwise stated)
Saturday
Dundee v Hamilton, Motherwell v Inverness CT, Rangers v Partick Thistle, St Johnstone v Aberdeen
Sunday
Ross County v Celtic (1230)