Both sides head into the fourth-round tie without a manager at the helm, after Terry Butcher quit the Highlands for Hibernian and Allan Moore was sacked by the Greenock outfit last weekend.
However, their respective fortunes could not be more different ahead of the clash at the Caledonian Stadium.
Inverness sit second in the Scottish Premiership, while Morton are languishing at the bottom of the Championship and still smarting from the 5-1 home defeat to Livingston that ultimately cost Moore his job.
Morton did manage to pull off one of the shocks of the season, though, when they defeated Celtic in the League Cup to end the Scottish champions' hopes of a domestic treble.
Watkins said: "We can't get complacent just because they are in a lower league.
"We've got to treat this like every other game.
"We want to do well in every game and in every competition.
"It's a good opportunity to go on a run and who knows where we can get to."
Inverness have continued their fine form under caretaker boss Duncan Shearer, despite the departure of Butcher.
Watkins said: "We've got big characters in the squad, like Richie (Foran) our captain, who gets everyone going.
"All the boys have a good attitude and we want to keep this run going.
"It's been good, positive. Everyone is looking forward to the next game in the cup now.
"We want to go on a good run in the cup as well."
Watkins believes Caley Thistle can take plenty of confidence from last week's win at St Johnstone.
The midfielder said: "They are a good team but I don't think they troubled us really.
"That shows how well we played defensively. We got the win and we deserved it."
Morton's interim-manager David Hopkin takes charge of the Greenock men for the first time and has been denied the services of striker Kabba-Modou Cham.
Cham was handed a two-game ban after being dismissed against Livingston last Saturday.
Scott Taggart is ready to return after injury, but skipper Mark McLaughlin is doubtful and Reece Hands (pelvis) and David O'Brien (shoulder) are still out.
Hopkin said: "This is a tough tie, but I want us to go out and put on a performance that starts to build some belief.
"The players were a bit down with the manager Allan Moore leaving, but we have to start bouncing back somewhere."
- Sports & Recreation
- Terry Butcher
- Scottish Premiership