The 31-year-old Croatian midfielder joined the Gers on a two-year deal last week after a short stint in the US second tier.
Speaking to Big Apple Soccer, New York Cosmos head coach Giovanni Savarese has admitted his disappointment that the club could not convince new Rangers signing Niko Kranjcar to extend his spell in the USA.
Kranjcar, 31, originally began training with the Cosmos in February after being released by Dynamo Kiev a few weeks earlier, before later opting to sign a short-term contract with the US second-tier outfit for the 10-game NASL Spring Season.
The Croatian midfielder went on to feature seven times for the club, recording one and an assist, but missed the final three games of the campaign with a quad strain.
The team did hold talks with the former Tottenham Hotspur and Queens Park Rangers star about extending his deal into the Fall Season, but an offer to return to the UK from Rangers proved too good to turn down.
The veteran playmaker ultimately joined the Scottish Premiership side on a two-year contract last week, and Savarese expects him to make a big impact at Ibrox.
“We tried to keep him here," the Cosmos boss told Big Apple Soccer. "We did make an offer. We did try to sit down and figure things out and possibly we could keep him here.
“But also we have to understand that this move for him has been a very important move. That values the player even more so, that from our team he is still able to compete at the Premiership level.
"He's still young. We were very content to have him here. For sure we would have loved to have had him a little bit longer. But also he also has shown us tremendous qualities as a person, as a player.
“We're very happy for him. We wish him the best. I have no doubt that he will be a very impactful player for Rangers."
Kranjcar incidentally returned to the States with Rangers on Monday for their pre-season training camp in Charleston, South Carolina, which will conclude with a game against USL Pro side Charleston Battery on 6 July at MUSC Health Stadium.
The 81-times capped international will become the third Croatian to wear the Gers shirt after Nikica Jelavic and Dado Prso, and he is hoping to achieve the same level of success his compatriots had during their time in Glasgow.
“Hopefully I can achieve as much as they did," Kranjcar told the Herald Scotland at his official unveiling last week. “Obviously they were both fantastic goalscorers but great characters and they always played with 100%.
“I’ll definitely do my best to repeat that. [Nikica] was delighted for me, he congratulated me. He said I’m sure I’m going to enjoy it and do well.
“I knew [about the Rangers fans] growing up, even back home you watch the Old Firm on TV, I knew a lot about the support that Rangers has as a football club.”