Manager Chris Coleman's team are disrupted by absent players, including Real Madrid forward Gareth Bale.
But Swansea's Williams wants Wales to put down markers ahead of Euro 2016.
"We've missed players before and everyone has come in and done pretty well, so we'll be looking for something similar again," he said.
"When you play against one of the other home nations it's never really a friendly - you always want to win.
"We'll be wanting to get two wins out of the next two games and good performances."
Bale, Aaron Ramsey, Ben Davies and Hal Robson-Kanu are among eight players out injured for Wales.
Northern Ireland are without defender Chris Baird and midfielder Chris Brunt, who will miss Euro 2016.
Wales face Northern Ireland in the Cardiff City Stadium before travelling to Kiev.
"There are a few players out so there are new faces in so they've got something to prove," added Williams.
"For the rest of us it's about trying to get some momentum built towards the Euros. With the tournament coming up everyone wants to show what they can do for the team."
Williams has already had a season to remember, helping Wales qualify for their first major finals since the 1958 World Cup and leading Swansea City's battle to avoid relegation from the Premier League.
The Swans are 10 points clear of the drop zone after their 1-0 win over Aston Villa, but Williams admits it has been mentally draining.
But the struggle has also stopped his mind wandering to this summer's tournament in France.
"The Euros have been at the back of the mind, but it's difficult to take your eye off the Premier League," he said.
"It's been a tough season mentally - with Swansea as well as with Wales."
But Williams said the thought of taking a break had not crossed his mind.
"But I'll be on the pitch as much as possible," he added.
"I take pride in that and I'll lead the players as much as I can in the next two games."
Wales captain Ashley Williams wants two wins and good performances in friendly matches against Northern Ireland on Thursday and Ukraine on Monday.