even among CRTs there are variations in the processing and other component factors that cause differing amounts of input delay. there just tends to be less variation and a much lower max, which is why generally there's an "as long as it's CRT, it's good" attitude; players tend to be able to very easily adjust to the differences between most CRTs—if they even notice the minute differences at all. so it's definitely possible/likely that your TV at home feels different from the one you played on at the venue, BUT what tauKhan said is also true.
for something like wavedashing, no amount of input delay should affect your ability to execute the technique. any lag from the display should be consistent. so doing the wavedash input series with your hand should produce a wavedash on basically any TV; it would just appear to happen at different times, depending on the display.
input lag should only really affect your techskill when you're doing something where you rely on a visual cue, since the delayed display necessarily delays your reaction and subsequently whatever input you need to do. for anything that you've reduced to muscle memory, you'll always get the timing right and nothing having to do with the display should affect your execution.
so if you noticed the difference based on something like wavedashing (which presumably, you can do at home with your eyes closed), your techskill issue wasn't caused by the difference in display lag between the two TVs—even if there was one.
it was your first tourney. anxiety/pressure is a totally real thing. alot of people really don't respect the amount of stress that your mind and body are under and the really foreign chemical reactions that are happening inside of you that affect all sorts of aspects of your play. obviously, you don't get to play in tournament just all the time, but one thing that i've always stressed whenever i'm teaching someone Melee is that they practice new techniques in matches as much as they practice them solo in the lab. so get a practice partner. it's not the same environment as playing in tourney, but playing in a match is at least closer than running around in training mode all by yourself in the no-pressure comfort of your bedroom. and it's important to get your hands used to doing this stuff when you are under the effects of adrenaline or stressed out a little or feeling under pressure because you're down a stock or at high % or whatever.
