The North Berwick woman was speaking as her leadership was lauded by players after she became the first European captain to record back-to-back wins in the biennial event.
Matthew, who played in the match nine times, joined US duo Judy Rankin (1996 and 1998) and Inkster (2015 and 2017) as the only two-time winning captains in the contest.
She achieved the feat as Europe, having triumphed in dramatic fashion in her first stint at Gleneagles in 2019, came out on top 15-13 in another nail-biter at Inverness Club in Toledo, Ohio.
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The next Solheim Cup will be played in Spain in 2023, but Matthew insisted it is time for her to step aside, with Gleneagles match-winner Suzann Pettersen, who was an assistant captain on this occasion, likely to be one of the main contenders.
“We have so many good past players, and I think everyone deserves their chance to be captain,” said Matthew, who was hoisted into the air by her players on the 18th green after this latest triumph.
“I think to be part of the Solheim, I was lucky enough to play in nine and I've captained two, and I've had a fantastic time.
“It's the best week I've had every two years, and to have been involved with it now for over 20 years, I'm sure I'll be there watching, but it's someone else's turn.”
Matthew’s Solheim Cup legacy was summed up by Swede Anna Nordqvist, the AIG Women’s Open champion, who was a team-mate of the Scot’s before she became captain.
“I think we all look up to Catriona Matthew a lot,” she said. “She's been a great role model for all of us. I've had the opportunity to play with her on the team, which has been a huge honour. I obviously watched her growing up.
“Playing I think the first two rounds of the British Open the year when Catriona won (in 2009), seeing her shoot 29 on the back nine of Lytham St Anne's is still probably one of the best rounds I've ever seen. Seeing her win obviously just after having her second baby is still amazing.
“She's been a great Solheim Cup player. I remember watching her in 2003 in Barsebäck when I was outside the ropes and could only dream about making one team, and now I've made a few.
“But having her as a captain the last two years and seeing the way she has led the team, the way she's brought all the girls together, hands down this is the best team I think Europe ever had.
“She did have to make a few hard decisions, leaving a few other players that have been playing good out.
“But just the calm that she has around her, the confidence she has in all the players, the way everything is thought out and how easy her and the rest of the assistant captains make it for us, it's been an honour to play for her as a captain the last two Solheim Cups.”
The triumph in Toledo was only the second time that Europe had won on US soil, with Matthew having clinched a 2013 victory in Colorado.
“I think the similarities were the rookies played so well,” said Matthew, referring to Ireland’s Leona Maguire, in particular, picking up four-and-a-half points out of five and Finland’s Matilda Castren holing a crucial 10-foot putt on the final green in the singles.
“I remember in Colorado watching on that Saturday afternoon, I think all the rookies won 4-0 in that session.
“I think to win a Solheim Cup you have to have all your players playing well and you have to have all your players contribute points, and that's what we did this week.
“Our rookies stepped up under probably the most extreme circumstances with really having no European fans, so very proud of them.”
The visitors had led by three points after the opening session before seeing the Americans hit back on Sunday morning.
But, after rallying in the penultimate session to take a two-point advantage into the singles, Europe were not to be denied, even though Matthew admitted it got a “little dodgy” at one point.
“We got off to the dream start winning three and a half to a half. You could never have dreamed of getting off to a start like that,” she said of that opening session.
“Deep down, I knew the Americans were going to come back like they did, and I think the finish we had on Sunday, getting 2.5-1.5, just kind of buoyed our team.
“We had great momentum on Sunday night going into the singles, and I think having that two-point lead obviously was a great advantage to us playing away from home. I think you probably needed to have a little bit of a lead going into the singles.
“Obviously two years ago at Gleneagles was fantastic, but this time in America we were up against it. The Americans were a fantastic team this year. They played hard.
“We just perhaps holed a few more putts and were lucky we came out on top. I'd like to thank my team.
“I had a fantastic team, and the captains and our helpers and our caddies and just everyone, the LET staff. We've been one big team, and we've loved every moment of it.”