Last season’s top scorer Ings was sold to Aston Villa rather than risk him eventually departing on a free at the end of his contract.
The Saints, though, moved quickly to bring in cover, with Armstrong making the step up from the Sky Bet Championship while 19-year-old Armando Broja has come in on a season-long loan from Chelsea.
Armstrong attracted plenty of interest during the summer window and Hasenhuttl believes the 24-year-old can settle to take on the leading frontman role at St Mary’s.
“He is definitely coping with it. He has the same number on his shirt (as Ings did) and he doesn’t care because he knows he can score goals,” Hasenhuttl said.
“It is on us to bring him in the position to go there and we know that Ingsy was here for two years until he started scoring for us.
“We have enough time, Che Adams has enough time to develop himself and we know that it is not so easy to step into the Premier League and immediately be there.
“The young lads will get all the time they need to develop.”
With defender Jannik Vestergaard moving to Leicester, Hasenhuttl has lost another key man.
But the Austrian coach accepts the arrivals and departures are all part of a manager’s remit at a club of Southampton’s standing.
“This is the way we have to go. It is always like starting again, again and again,” Hasenhuttl said.
“Develop players, they leave and we go again. It is our job and it is not tougher than the years before.
“It is a pleasure for me to work with this group, it is a pleasure for me to look to make them better.
“We have a few very good young guys with potential and the key is that we have the quality.
“If you bring the quality to shine, then you can still have a very good season.”
Hasenhuttl accepts there is little a club can do now when faced with a player moving towards the end of their current deal, as was the case with both Ings and Vestergaard.
“One thing that is for sure, when players are going into the last one or two years in the contract, the power moves to the players and away from the clubs,” the Southampton boss said.
“This is because of the rule we have since Bosman that players at the end of the contract are completely free.
“This is a horrible situation for a lot of clubs in football and it leads us to this situation we are in at the moment where there are a lot of clubs struggling.
“We are not the only club who tries to extend contracts from players. They one time cost a lot of money and then don’t want to stay with you anymore.
“You have to add the wages to the transfer fee you paid for them and this is the total amount of money that you have spent for this player.”
Hasenhuttl continued: “For us it is very important that we get something for players when they are coming in the last year. That leads us to the situation we have been in.
“That doesn’t mean that we want to sell under the price we have because we developed these players, we make them better, they are on maybe some of the best levels of their careers like Ingsy at the moment. He was never that good like he has been with us.
“Yes, it is also understandable for the player that they want to go somewhere else and make more money or whatever and take this instead of being a legend in this club forever.
“This is modern football, this is how it changed. We as managers have to accept it and find alternatives. This is our goal.”