The Real Madrid midfielder spoke out in the aftermath of the 2-0 defeat to Chile on Wednesday, a result which - coupled with their 5-1 hammering by Netherlands - meant a swift exit for the defending champions.
There have been reports the comments did not go down well with his team-mates, and fellow midfielder Santi Cazorla dismissed them out of hand at Friday's press conference.
After attempting to clarify what he meant, Alonso insisted he still had a good relationship with the other members of the dressing room.
He told Spanish radio station El Larguero: "I have not felt alone because the feeling is very similar for all my colleagues that I have spoken to.
"There are people who needed a small statement or any excuse to make a debate. The collective feeling is that we have lacked the necessary tension.
"The atmosphere is very good and I have no problem. My relationship is good with everybody."
While his own international future remains in doubt, the 32-year-old conceded Spain need a re-think ahead of the European Championship qualifying.
"We had a brilliant cycle that has made history, but now, after this defeat, we will change things," he added.
"We have been very successful but maintaining this is very complicated. We need to take as much as possible from this painful defeat."
In elimination, Spain became the fifth world champions to fall at the first hurdle. Their final group game comes against Australia in Curitiba on Monday June 23.