"We are absolutely delighted to get another win," Smyth admitted to IrishRugby.ie afterwards.
"It was always going to be a very difficult game with the runs the two teams were on. At the end, one team was going to come out with a fourth win and we wanted to be that team.
"The weather had a huge impact in the second half, it was difficult for both sides to play a bit of rugby but that is why the try before half-time was so vital. It gave us a bit more confidence going into the second half."
Smyth added: "To be honest the past few years we have been on the wrong side in games like this, so when you win you have got to enjoy the feeling.
"At the same time, there's a lot more games to go and I am sure there will be a lot more twists and turns along the way.
"We are grateful for what we have at the moment, but we are realistic as well. We haven't even reached the autumn internationals so nobody is going to be getting carried away."
Impressive flanker Paul Nash was similarly happy with how Mary's survived against Dolphin.
"We are extremely happy with the way things are going. I'm not going to say we expected to have four wins at this stage, but it is very nice to know that we are on the right track," he said.
"It's extremely encouraging for us that this game went our way.
"It was a real battle in the second half with the weather - the thunder and lightning made it tougher - so to come through with a win was brilliant for us."
Dolphin coach Steve Forde gave an honest verdict, admitting that the home side shaded the battle.
"We are still in a good position, absolutely, they have got to come back down to us in Cork," he said.
"This was our second away game in the AIB League, St. Mary's have done well so far and I thought they deserved their win.
"I think that we are going well, we have a good group of boys. We have to learn from this defeat and we have to learn from the mistakes we made and make sure we get better in our next game.
"We have a short window to turn around for next week's game against Belfast Harlequins in the AIB Cup. We have Garryowen away in our next AIB League match - they are all tough games at this level."
Click here for a full St. Mary's College v Dolphin match report.