Mikel Arteta said he had doubts when he became Arsenal boss last December that captain Pierre-Emerick Aubameyang would agree a new contract.
The Gabon striker, 31, signed a three-year deal on Tuesday to end months of speculation over his Gunners future.
Aubameyang, whose previous deal expired next summer, has scored 72 times in 111 Arsenal games, including both goals in August's FA Cup final win over Chelsea.
"When I joined, I wasn't as positive as I was in recent weeks," said Arteta.
"Obviously, financially we were in a position that it was difficult to get where we wanted to get. I think Auba had his doubts as well at the time, but things evolved in a natural way.
"I had the feeling that the club wanted to move forward, I had the feeling that Auba wanted to stay here and we were just trying to apply those things together and that sometimes takes time.
"But the outcome is what we both wanted, so we are happy."
'We had to balance squad plans with finances'
While Aubameyang has remained with the club, long-serving goalkeeper Emiliano Martinez joined Aston Villa on Wednesday.
The 28-year-old Argentine spent 10 years with the club - playing in the FA Cup final win as first choice Bernd Leno was injured - but Arteta says his £17m departure could help fund new signings.
"We have to find some balance between what we want to achieve with the squad and our finances, and it gets to a point where you have to make a decision whether to achieve certain things you have to sacrifice others," he said.
"But time will tell whether we are weaker or not. Obviously the recruitment we are planning to do to try to get our second goalkeeper hopefully will bring us a really good performance level."
Arteta also suggested a change in Martinez's expectations after playing his part on the pitch, led to a situation where neither he nor Leno would be happy as second choice.
"I was very clear with both of them that it wasn't a one and a two, they had to compete for their place like any other position in the team," he added.
"Bernd was superb before he got injured at Brighton and Emi was absolutely excellent with all the games he played and how much he helped us win the trophies.
"But at the end of the day that created a big competition, some big expectations from both of them and we had to deal with that."