Koeman was dismissed in October last year, with Barcelona ninth on the table with just four wins in their opening 11 La Liga games.
They were also six points behind Real Madrid when Koeman left.
Fast forward six months later, Barcelona are second on the table and 15 points behind Real Madrid going into this weekend's fixtures.
Koeman has rued a lack of support from the Barcelona hierarchy during his time; something he craves for Xavi but says their progress has somewhat stalled.
"I can write a book [about my time at Barca]. Many things happened to us,” Koeman told a news conference.
“Covid issue, lack of president for a while, I had to answer all kinds of questions, not being able to sign the players we wanted, [financial] fair play complications, without Leo Messi from one day to another, losing [Antoine] Griezmann on the last day of the market.”
“Sure, they have improved in some things. They have signed three strikers or three players who can play up front,” he said.
“It is not good to compare. When I left, Barcelona was eight points away and now almost double. It is not good to compare.
“Xavi's task It's just as complicated as me. This is the reality of Barcelona today. It needs time to return to what it was and, therefore, I ask for peace of mind and not to think that we haven't won titles. We have to think long-term, trust and support the coach.”
